A094905 - OEIS

%I #14 Dec 15 2022 15:25:34

%S 1,7,55,541,7585,157231,4452247,157484725,6594785281,317357589655,

%T 17222102537911,1039632137764237,69073193451776545,

%U 5007661199176196671,393324947394545293975,33268708968518818629541

%N Expansion of e.g.f.: exp(6*x)/(1-6*x)^(1/6).

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

%F E.g.f.: exp(6*x)/(1-6*x)^(1/6).

%F a(n) = Sum_{k = 0..n} A046716(n, k)*6^k.

%F Conjectured to be D-finite with recurrence: a(n) +(-6*n-1)*a(n-1) +36*(n-1)*a(n-2) = 0. - _R. J. Mathar_, Nov 15 2019

%F a(n) ~ sqrt(Pi) * 2^(n + 1/2) * 3^n * n^(n - 1/3) / (Gamma(1/6) * exp(n - 1)). - _Vaclav Kotesovec_, Nov 19 2021

%t With[{nn=20},CoefficientList[Series[Exp[6x]/Surd[1-6x,6],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 15 2022 *)

%Y Cf. A046716.

%Y Cf. A000522, A081367, A094822, A094856, A094869.

%K nonn

%O 0,2

%A _Philippe Deléham_, Jun 16 2004