A094905 Expansion of e.g.f.: exp(6*x)/(1-6*x)^(1/6).

1, 7, 55, 541, 7585, 157231, 4452247, 157484725, 6594785281, 317357589655, 17222102537911, 1039632137764237, 69073193451776545, 5007661199176196671, 393324947394545293975, 33268708968518818629541

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..15.

Formula

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

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

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

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

Mathematica

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

Crossrefs

Cf. A046716.

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

Sequence in context: A123784 A091695 A002882 * A178922 A306046 A362080

Adjacent sequences: A094902 A094903 A094904 * A094906 A094907 A094908

Keyword

nonn

Author

Philippe Deléham, Jun 16 2004

Status

approved