A352114 Expansion of e.g.f. (1 - log(1 - 4*x))^(1/4).

1, 1, 1, 17, 129, 2529, 42753, 1080561, 28269825, 910318785, 31733067777, 1260881785041, 54451914027393, 2588888715388065, 132887134408562433, 7371812870053439409, 437841346658159352321, 27782111830252836998529, 1873198439610729939408897

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} (-4)^(n-k) * (Product_{j=0..k-1} (-4*j+1)) * Stirling1(n,k).

a(n) ~ n! * 2^(2*n-2) / (log(n)^(3/4) * n) * (1 - 3*(gamma + 1)/(4*log(n))), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 05 2022

Mathematica

m = 18; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 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((1-log(1-4*x))^(1/4)))
(PARI) a(n) = sum(k=0, n, (-4)^(n-k)*prod(j=0, k-1, -4*j+1)*stirling(n, k, 1));

Crossrefs

Cf. A352075, A352113.

Cf. A352073.

Sequence in context: A159563 A341397 A229516 * A279637 A179818 A138640

Adjacent sequences: A352111 A352112 A352113 * A352115 A352116 A352117

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2022

Status

approved