A094911 Expansion of e.g.f. exp(7*x)/(1-7*x)^(1/7).

1, 8, 71, 778, 12125, 284012, 9241891, 378595022, 18409947641, 1029827400400, 64998958518719, 4565303338264082, 353016345110857429, 29793105387299603252, 2724646021507044539675, 268374407984059193374678

Offset

0,2

Comments

Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n), A094869(n), A094905(n) for x = 1, 2, 3, 4, 5, 6 respectively.

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*7^k.

Conjectured to be D-finite with recurrence: a(n) +(-7*n-1)*a(n-1) +49*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2019

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 7^n / (Gamma(1/7) * exp(n-1) * n^(6/7)). - Vaclav Kotesovec, Nov 19 2021

Prog

(PARI) my(x='x+O('x^20)); Vec(serlaplace(exp(7*x)/(1-7*x)^(1/7))) \\ Michel Marcus, Jan 23 2023

Crossrefs

Cf. A046716, A000522, A081367, A094822, A094856, A094869, A094905.

Sequence in context: A225033 A075506 A334670 * A294166 A203008 A235128

Adjacent sequences: A094908 A094909 A094910 * A094912 A094913 A094914

Keyword

nonn

Author

Philippe Deléham, Jun 17 2004

Extensions

Corrected by D. S. McNeil, Aug 20 2010

Status

approved