A094822 E.g.f.: exp(3x)/(1-3x)^(1/3).

1, 4, 19, 118, 1021, 12088, 183727, 3389242, 73156249, 1804349548, 50009179819, 1537920654526, 51952155415381, 1911990785926432, 76137201611236999, 3261400435090171522, 149530099101901409713, 7305923490645888605908, 378947686822932957638851

Offset: 0

Author

Philippe Deléham, Jun 12 2004

Keywords

• nonn

Comments

Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n) for x = 1, 2 respectively.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[3x]/Surd[1-3x,3],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 28 2018 *)

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*3^k.

a(n) ~ Gamma(2/3)*3^(n+1/2)*n^(n-1/6)/(sqrt(2*Pi)*exp(n-1)). - Vaclav Kotesovec, Jun 15 2013

Conjecture: D-finite with recurrence: a(n) +(-3*n-1)*a(n-1) +9*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 14 2019

Extensions

Corrected and extended by Harvey P. Dale, Jul 28 2018