A352123 Expansion of e.g.f. (2 - exp(-4*x))^(1/4).

1, 1, -7, 73, -1135, 24241, -659767, 21796153, -846456415, 37772943841, -1904103268327, 106992035096233, -6630198107231695, 449171668238551441, -33024202381308836887, 2618743082761141212313, -222782402553043700662975, 20238957866498067052271041

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (-4)^(n-k) * (Product_{j=0..k-1} (-4*j+1)) * Stirling2(n,k).

a(n) ~ n! * (-1)^(n+1) * Gamma(1/4) * 2^(2*n - 9/4) / (Pi * n^(5/4) * log(2)^(n -1/4)). - Vaclav Kotesovec, Mar 06 2022

Mathematica

m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-4*x])^(1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-4*x))^(1/4)))
(PARI) a(n) = sum(k=0, n, (-4)^(n-k)*prod(j=0, k-1, -4*j+1)*stirling(n, k, 2));

Crossrefs

Cf. A352121, A352122.

Cf. A352114.

Sequence in context: A258379 A325930 A360544 * A364938 A134281 A360934

Adjacent sequences: A352120 A352121 A352122 * A352124 A352125 A352126

Keyword

sign

Author

Seiichi Manyama, Mar 05 2022

Status

approved