A375953 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(5/2).

1, 5, 40, 430, 5770, 92590, 1726940, 36682200, 873793620, 23061929940, 667868085360, 21052931727240, 717531427466280, 26289935772108120, 1030422613932910800, 43018144091244322560, 1905711682795871222160, 89284805444478025826640

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A088500, A367474, A367475, A375945.

Cf. A001147.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(5/2),{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+2)*abs(stirling(n, k, 1)))/3;

Formula

a(n) = (1/3) * Sum_{k=0..n} A001147(k+2) * |Stirling1(n,k)|.