A375905 E.g.f. satisfies A(x) = (1 - log(1 - x * A(x)^(1/3)))^3.

1, 3, 15, 111, 1116, 14352, 226176, 4233492, 91936080, 2274815712, 63220205736, 1950659365608, 66187523184048, 2450020566119760, 98269427218682880, 4246150991775421824, 196657057172519603712, 9719485198364207149056, 510628699670802850684800

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A138013.

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

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

Prog

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

Crossrefs

Cf. A138013, A375904.

Sequence in context: A360864 A201339 A370877 * A254789 A112936 A001063

Adjacent sequences: A375902 A375903 A375904 * A375906 A375907 A375908

Keyword

nonn

Author

Seiichi Manyama, Sep 02 2024

Status

approved