A365604 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x)).

1, 5, 45, 610, 11020, 248870, 6744350, 213233400, 7704814200, 313199930400, 14146162064400, 702826758144000, 38093116667766000, 2236695336601458000, 141433354184701746000, 9582086196220281456000, 692463727252196674560000

Offset: 0

Author

Seiichi Manyama, Sep 11 2023

Keywords

• nonn

Crossrefs

Column k=5 of A320080.

Cf. A347022, A365601, A365602, A365603.

Cf. A094418, A365588.

Programs

Mathematica

a[n_] := Sum[5^k * k! * StirlingS1[n, k], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
With[{nn=20},CoefficientList[Series[1/(1-5*Log[1+x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 05 2025 *)

PARI

a(n) = sum(k=0, n, 5^k*k!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} 5^k * k! * Stirling1(n,k).

a(0) = 1; a(n) = 5 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).