A008494 Expansion of (1-x^12) / (1-x)^12.

1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716, 705432, 1352077, 2496132, 4457322, 7725796, 13036530, 21469812, 34584914, 54595476, 84596733, 128856520, 193184004, 285392328, 415873822, 598309152, 850534752, 1195596128, 1663018149

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Programs

GAP

Concatenation([1], List([1..40], n-> (604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10)/302400 )); # G. C. Greubel, Nov 07 2019

Magma

[1] cat [(604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10)/302400: n in [1..40]]; // G. C. Greubel, Nov 07 2019

Maple

1, seq((604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10)/302400, n=1..40); # G. C. Greubel, Nov 07 2019

Mathematica

Table[If[n==0,1,(604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10)/302400], {n,0,40}] (* G. C. Greubel, Nov 07 2019 *)

PARI

Vec((1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4) / (1 - x)^11 + O(x^30)) \\ Colin Barker, Jan 06 2017

Sage

[1]+[(604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10)/302400 for n in (1..40)] # G. C. Greubel, Nov 07 2019

Formula

From Colin Barker, Jan 06 2017: (Start)

a(n) = (604800 + 2286636*n^2 + 696905*n^4 + 39963*n^6 + 495*n^8 + n^10) / 302400 for n>0.

G.f.: (1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4) / (1 - x)^11.

(End)

E.g.f.: -1 + (604800 +3024000*x +8467200*x^2 +8265600*x^3 +4170600*x^4 + 1161720*x^5 +194460*x^6 +19740*x^7 +1245*x^8 +45*x^9 +x^10)* exp(x) / 302400. - G. C. Greubel, Nov 07 2019