A373861 a(n) = Sum_{k=0..n} k^(2*n) * |Stirling1(n,k)|.

1, 1, 17, 923, 107724, 22369324, 7385651720, 3597082257152, 2449105468081600, 2238708422118782376, 2661994302285967390224, 4014423110086784061347592, 7519716937006429200213786240, 17194081369411703462470895338272

Offset: 0

Author

Seiichi Manyama, Jun 19 2024

Keywords

• nonn

Crossrefs

Cf. A229261, A351183, A373856.

Programs

Mathematica

Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k!,{k,0,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)

PARI

a(n) = sum(k=0, n, k^(2*n)*abs(stirling(n, k, 1)));

Formula

E.g.f.: Sum_{k>=0} (-log(1 - k^2*x))^k / k!.