Polynomial Sequences

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Problem

Given is a sequence of integers, which follow a specific polynomial progression. Your job is to determine the next number in the sequence.

Further information:
-The sequences will be given as a space separated list. The first term is n=1, the second term is n=2, etc.
-Individual sequences are separated by a new line.
-The polynomials used will be between the order of 2 and 6.
-Enough terms will be given to identify each sequence uniquely: order 2 will have at least 3 terms, order 3 will have at least 4 terms, etc.
-All polynomial coefficients will be integer.

Options

now post-mortem time, all source codes will be revealed

Sample input:_

1 4 9
1 8 27 64
1 16 81 256 625
1 32 243 1024 3125 7776
1 64 729 4096 15625 46656 117649

Sample output:

16
125
1296
16807
262144

Sample input:_

4 61 284 859 2044 4169
2 16 72 224 550
2 19 70 173 346
5 14 27 44 65 90
1 -22 -109 -326 -763
5 6 -1 -22
3 37 155 435 979
5 3 -9 -37
0 -10 -34 -78
6 66 300 900 2130 4326

Sample output:

7636
1152
607
119
-1534
-63
1913
-87
-148
7896

Sample input:_

9 113 717 2775 8033 19269 40533 77387
8 53 214 617 1436 2893
6 7 -26 -147 -434 -989 -1938
5 5 -3 -25
8 62 278 842 2012 4118 7562
8 20 20 -34 -208 -592 -1300 -2470
8 52 236 734 1792
3 27 -199 -2193 -10401 -34597 -93003 -216129 -451333
9 243 2485 13437 50241 148159 370413
5 18 45 92 165 270
9 35 91 189 341 559
10 130 830 3298 9802 24050 51550 99970 179498
5 6 -27 -148 -435 -990 -1939 -3432
6 83 640 2781 8666 21871 47748 93785
2 48 558 3296 13050 40032 102998
7 169 1475 7195 25039 70037 168139 360535 708695
8 29 84 191 368 633
4 30 96 220 420 714 1120
6 29 82 177
8 222 2376 13100 49440 146538 367472 815256 1647000

Sample output:

137145
5258
-3431
-67
12818
-4264
3728
-868101
820185
413
855
303202
-5643
169966
233088
1300129
1004
1656
326
3090230

Ranking

Ruby _

RankUserSizeTimeDateStatistics
1ksk530.09522008/12/10 23:15:460B / 25B / 24B
2flagitious530.08092008/12/11 13:49:050B / 25B / 24B
3flagitious(W0)540.12082008/12/11 13:59:050B / 24B / 26B
4leonid570.10872008/12/11 11:33:000B / 26B / 29B
5primo680.14332008/12/09 21:07:390B / 34B / 31B
6tabasa4230.09462008/12/10 08:47:352B / 305B / 113B

Perl _

RankUserSizeTimeDateStatistics
1primo500.13362008/12/20 05:50:360B / 20B / 26B
2tails (primo)450.05542016/01/07 19:20:350B / 19B / 23B

Python _

RankUserSizeTimeDateStatistics
1hallvabo940.22662008/12/11 10:04:550B / 55B / 38B
2primo950.24792008/12/09 19:36:550B / 54B / 39B
3hirose990.27832008/12/11 11:57:150B / 57B / 40B
4primo(recursion)1030.36762008/12/12 22:28:290B / 61B / 33B
5recursive1030.84062008/12/21 00:23:020B / 59B / 31B

PHP _

RankUserSizeTimeDateStatistics
1primo1100.22762008/12/09 23:45:290B / 48B / 60B
2teebee(primo,sinpamov)1040.05822017/04/14 08:00:530B / 50B / 52B

Common LISP _

RankUserSizeTimeDateStatistics
1kozima1180.67412009/02/21 10:20:350B / 67B / 46B

Arc _

RankUserSizeTimeDateStatistics
1murky-satyr8811.54742009/11/01 00:15:480B / 46B / 33B

JavaScript _

RankUserSizeTimeDateStatistics
1nn850.15042008/12/09 22:55:540B / 40B / 44B
2murky-satyr850.09452009/01/04 08:53:500B / 46B / 35B

BASIC _

RankUserSizeTimeDateStatistics
1pooq2270.07392008/12/10 18:53:280B / 165B / 23B

J _

RankUserSizeTimeDateStatistics
1I., S.(cheat)460.12262010/11/08 07:45:010B / 16B / 28B
2I., S.530.13192010/11/07 22:00:300B / 19B / 32B
3pooq1190.15042010/07/08 15:56:530B / 54B / 54B

C _

RankUserSizeTimeDateStatistics
151b1280.04702008/12/14 03:39:510B / 60B / 68B
2Purika1440.05752008/12/20 18:12:500B / 69B / 75B
351b1200.06452009/01/10 15:59:180B / 53B / 67B

D _

RankUserSizeTimeDateStatistics
151b1440.09112009/01/25 21:52:470B / 78B / 64B

Pascal _

RankUserSizeTimeDateStatistics
1uru2610.07372008/12/14 02:54:350B / ?B / ?B
2uru2540.00052008/12/23 19:36:080B / ?B / ?B

AWK _

RankUserSizeTimeDateStatistics
1nn430.16212008/12/12 22:53:430B / 19B / 24B

Postscript _

RankUserSizeTimeDateStatistics
1yshl(bin)951.21022008/12/14 05:02:4447B / 31B / 17B
2yshl1921.20072008/12/14 05:02:360B / 144B / 18B
3tails (bin yshl)730.26652017/04/14 17:24:4835B / 20B / 18B
4yshl(bin)751.18752008/12/27 02:28:0642B / 21B / 12B
5tails (ascii yshl)1400.25212017/04/14 09:44:190B / 105B / 17B
6yshl1431.17262008/12/27 02:27:500B / 107B / 16B

GolfScript _

RankUserSizeTimeDateStatistics
1flagitious280.28892008/12/11 13:08:000B / 7B / 21B
2tails260.12552016/01/08 15:58:470B / 2B / 24B

goruby _

RankUserSizeTimeDateStatistics
1murky-satyr440.10612010/01/03 22:46:030B / 20B / 21B

Groovy _

RankUserSizeTimeDateStatistics
1murky-satyr863.64852009/12/27 03:05:170B / 54B / 28B
2nn977.23682009/11/07 12:40:040B / 58B / 35B

Language Ranking_

RankLangUserSizeScore
1GolfScripttails2610000
2AWKnn436046
3gorubymurky-satyr445909
4Perltails (primo)455777
5JI., S.(cheat)465652
6Rubyksk534905
7Postscripttails (bin yshl)733561
8JavaScriptnn853058
9Groovymurky-satyr863023
10Arcmurky-satyr882954
11Pythonhallvabo942765
12PHPteebee(primo,sinpamov)1042500
13Common LISPkozima1182203
14C51b1202166
15D51b1441805
16BASICpooq2271145
17Pascaluru2541023

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