A375946 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(4/3).

1, 4, 32, 372, 5652, 105936, 2360712, 60956472, 1789413864, 58850914752, 2143354213728, 85629122177760, 3723269780412000, 175035687610956480, 8846458578801144000, 478330017277120767360, 27551501517174431852160, 1684176901225092936990720

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A052801, A375945.

Cf. A354263, A365575, A375951.

Cf. A007559.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (1 + 3 * Log[1-x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k+1)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} A007559(k+1) * |Stirling1(n,k)|.