A095176 E.g.f.: exp(9x)/(1-9x)^(1/9).

1, 10, 109, 1432, 26497, 754894, 30787885, 1603546156, 99602138593, 7128277455538, 576063289419661, 51832424202980320, 5136461847251936929, 555721381650431686582, 65167921144448534609677

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), A094935(n) for x = 1, 2, 3, 4, 5, 6, 7, 8 respectively.

From Vaclav Kotesovec, Nov 19 2021: (Start)

In general, for k > 0, if e.g.f. = exp(k*x) / (1 - k*x)^(1/k), then a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * k^n / (Gamma(1/k) * exp(n-1) * n^(1 - 1/k)).

Equivalently, a(n) ~ n! * exp(1) * k^n / (Gamma(1/k) * n^(1 - 1/k)). (End)

Links

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

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*9^k.

D-finite with recurrence a(n) +(-9*n-1)*a(n-1) +81*(n-1)*a(n-2)=0. - R. J. Mathar, Aug 20 2021

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 9^n / (Gamma(1/9) * exp(n-1) * n^(8/9)). - Vaclav Kotesovec, Nov 19 2021

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[9x]/Surd[1-9x, 9], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 25 2020 *)

Crossrefs

Sequence in context: A190919 A095740 A075508 * A061749 A348466 A280566

Adjacent sequences: A095173 A095174 A095175 * A095177 A095178 A095179

Keyword

nonn

Author

Philippe Deléham, Jun 20 2004

Status

approved