A375900 E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/3)))^3.

1, 3, 21, 237, 3738, 76212, 1912350, 57099816, 1979628552, 78224586240, 3472089084072, 171098204829120, 9271248509444544, 548011290335056272, 35095593433694127696, 2421035179995679335360, 178997036386314294247680, 14121215676864610247122560

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052802.

E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (1 + log(1-x))) )^3.

a(n) = (3/(n+3)!) * Sum_{k=0..n} (n+k+2)! * |Stirling1(n,k)|.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x)))/x)^3))
(PARI) a(n) = 3*sum(k=0, n, (n+k+2)!*abs(stirling(n, k, 1)))/(n+3)!;

Crossrefs

Cf. A052802, A375899.

Cf. A354122.

Sequence in context: A375898 A302703 A334262 * A234855 A367375 A058562

Adjacent sequences: A375897 A375898 A375899 * A375901 A375902 A375903

Keyword

nonn

Author

Seiichi Manyama, Sep 01 2024

Status

approved