A375798 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x).

1, 1, 2, 9, 48, 340, 2820, 27720, 309120, 3897936, 54472320, 838918080, 14080651200, 256214724480, 5018771197440, 105361754097600, 2358985057228800, 56124276848640000, 1413738138502609920, 37591686093776855040, 1052149579611011481600

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * |Stirling1(n-k,n-2*k)|/(n-k)!.

a(n) ~ n! * (1 - r^2) / ((r^2 + 2*r - 1) * r^n), where r = 0.714556384743009681601449126434362887596497938663830826955917... (see A201750). - Vaclav Kotesovec, Sep 30 2025

Mathematica

nmax = 20; CoefficientList[Series[1/(1 + Log[1 - x^2]/x), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 30 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!);

Crossrefs

Cf. A007840, A375799.

Cf. A121452, A201750.

Sequence in context: A257544 A295944 A356632 * A224140 A360103 A382454

Adjacent sequences: A375795 A375796 A375797 * A375799 A375800 A375801

Keyword

nonn

Author

Seiichi Manyama, Aug 29 2024

Status

approved