A293986 Expansion of e.g.f. exp((1/(1-x)^7 - 1)/7).

1, 1, 9, 97, 1249, 19041, 338281, 6872929, 156878337, 3964344769, 109649487241, 3290138609121, 106344130171489, 3680908100971297, 135759417307847529, 5312294503297893601, 219710817062641086721, 9572694339517999983489, 438078249108592685152777

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..404

Formula

D-finite with recurrence: n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*a(n) + (-8*n^7 - 224*n^6 - 2576*n^5 - 15680*n^4 - 54152*n^3 - 105056*n^2 - 104544*n - 40320)*a(n + 1) + (28*n^6 + 756*n^5 + 8260*n^4 + 46620*n^3 + 142912*n^2 + 224784*n + 141120)*a(n + 2) + (-56*n^5 - 1400*n^4 - 13720*n^3 - 65800*n^2 - 154224*n - 141120)*a(n + 3) + (70*n^4 + 1540*n^3 + 12530*n^2 + 44660*n + 58800)*a(n + 4) + (-56*n^3 - 1008*n^2 - 5992*n - 11760)*a(n + 5) + (28*n^2 + 364*n + 1176)*a(n + 6) + (-57 - 8*n)*a(n + 7) + a(n + 8) = 0. - Robert Israel, May 25 2026

Maple

f:= gfun:-rectoproc({ n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*a(n) + (-8*n^7 - 224*n^6 - 2576*n^5 - 15680*n^4 - 54152*n^3 - 105056*n^2 - 104544*n - 40320)*a(n + 1) + (28*n^6 + 756*n^5 + 8260*n^4 + 46620*n^3 + 142912*n^2 + 224784*n + 141120)*a(n + 2) + (-56*n^5 - 1400*n^4 - 13720*n^3 - 65800*n^2 - 154224*n - 141120)*a(n + 3) + (70*n^4 + 1540*n^3 + 12530*n^2 + 44660*n + 58800)*a(n + 4) + (-56*n^3 - 1008*n^2 - 5992*n - 11760)*a(n + 5) + (28*n^2 + 364*n + 1176)*a(n + 6) + (-57 - 8*n)*a(n + 7) + a(n + 8), a(0) = 1, a(1) = 1, a(2) = 9, a(3) = 97, a(4) = 1249, a(5) = 19041, a(6) = 338281, a(7) = 6872929}, a(n), remember):
map(f, [$0..30]); # Robert Israel, May 25 2026

Prog

(PARI) my(N=66, x='x+O('x^N)); Vec(serlaplace(exp((1/(1-x)^7-1)/7)))

Crossrefs

Column k=8 of A291709.

Sequence in context: A194725 A386389 A218500 * A380639 A123821 A145509

Adjacent sequences: A293983 A293984 A293985 * A293987 A293988 A293989

Keyword

nonn

Author

Seiichi Manyama, Oct 21 2017

Status

approved