A094935 E.g.f.: exp(8x)/(1-8x)^(1/8).

1, 9, 89, 1073, 18321, 476473, 17484457, 813648417, 45054110369, 2872362067433, 206710159889529, 16558892507010961, 1460688620617834801, 140655075719488236057, 14678730623948132120009

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), A094911(n) for x = 1, 2, 3, 4, 5, 6, 7 respectively.

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*8^k.

D-finite with recurrence: a(n) +(-8*n-1)*a(n-1) +64*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2019

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 8^n / (Gamma(1/8) * exp(n-1) * n^(7/8)). - Vaclav Kotesovec, Nov 19 2021

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[8x]/Surd[1-8x, 8], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jan 25 2019 *)

Crossrefs

Sequence in context: A069573 A101679 A075507 * A258388 A296618 A230114

Adjacent sequences: A094932 A094933 A094934 * A094936 A094937 A094938

Keyword

nonn

Author

Philippe Deléham, Jun 18 2004

Status

approved