A375898 E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/3)))^3.

1, 3, 21, 234, 3627, 72498, 1780953, 52013118, 1762754655, 68060512458, 2950869169125, 142006584810918, 7513205987292243, 433548334132153698, 27102592662130603857, 1824854382978573444174, 131676307468686605671623, 10137713081262046098901050

Offset: 0

Author

Seiichi Manyama, Sep 01 2024

Keywords

• nonn

Crossrefs

Cf. A052894, A375897.

Cf. A226515.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(2-exp(x)))/x)^3))

PARI

a(n) = 3*sum(k=0, n, (n+k+2)!*stirling(n, k, 2))/(n+3)!;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052894.

E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (2 - exp(x))) )^3.

a(n) = (3/(n+3)!) * Sum_{k=0..n} (n+k+2)! * Stirling2(n,k).