A375904 E.g.f. satisfies A(x) = (1 - log(1 - x * A(x)^(1/2)))^2.

1, 2, 8, 52, 482, 5868, 88916, 1616032, 34300584, 833331600, 22815541872, 695254540704, 23343144376944, 856304206749600, 34078074674281920, 1462430515496217600, 67322828681189917440, 3309486192768294286848, 173034403244058605806080

Offset: 0

Author

Seiichi Manyama, Sep 02 2024

Keywords

• nonn

Crossrefs

Cf. A138013, A375905.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(1-log(1-x)))/x)^2))

PARI

a(n) = 2*(n+1)!*sum(k=0, n, abs(stirling(n, k, 1))/(n-k+2)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A138013.

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

a(n) = 2 * (n+1)! * Sum_{k=0..n} |Stirling1(n,k)|/(n-k+2)!.