A375947 Expansion of e.g.f. 1 / (1 + 4 * log(1 - x))^(3/2).

1, 6, 66, 1032, 20856, 516384, 15129600, 511880160, 19637499360, 842285112000, 39939749040960, 2074625404323840, 117151213971202560, 7145371319204666880, 468138620331976343040, 32788234887866638709760, 2444773199922430356833280

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A000407, A354241, A375950.

Programs

Mathematica

nmax=16; CoefficientList[Series[1 / (1 + 4 * Log[1-x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a000407(n) = (2*n+1)!/n!;
a(n) = sum(k=0, n, a000407(k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} A000407(k) * |Stirling1(n,k)|.