A375945 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(3/2).

1, 3, 18, 156, 1758, 24342, 399480, 7577700, 163090500, 3926104860, 104520733560, 3048811591680, 96695722690200, 3312942954681240, 121938065727180480, 4798400761979259120, 201030443703421854480, 8933622147642363338160, 419725992843354254228640

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A052801, A375946.

Cf. A088500, A367474, A367475, A375953.

Cf. A001147.

Programs

Mathematica

nmax=18; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k+1)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} A001147(k+1) * |Stirling1(n,k)|.

a(n) ~ n^(n+1) / (exp(n/2) * (exp(1/2) - 1)^(n + 3/2)). - Vaclav Kotesovec, Sep 06 2024