|
%I #14 Jan 30 2020 21:29:15
%S 1,4,19,118,1021,12088,183727,3389242,73156249,1804349548,50009179819,
%T 1537920654526,51952155415381,1911990785926432,76137201611236999,
%U 3261400435090171522,149530099101901409713,7305923490645888605908,378947686822932957638851
%N E.g.f.: exp(3x)/(1-3x)^(1/3).
%C Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n) for x = 1, 2 respectively.
%F a(n) = Sum_{k = 0..n} A046716(n, k)*3^k.
%F a(n) ~ Gamma(2/3)*3^(n+1/2)*n^(n-1/6)/(sqrt(2*Pi)*exp(n-1)). - _Vaclav Kotesovec_, Jun 15 2013
%F 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
%t With[{nn=20},CoefficientList[Series[Exp[3x]/Surd[1-3x,3],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 28 2018 *)
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 12 2004
%E Corrected and extended by _Harvey P. Dale_, Jul 28 2018
|
