A365603 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(4/5).

1, 4, 32, 404, 6924, 150000, 3927480, 120582360, 4246964280, 168767136000, 7468938047520, 364284571992480, 19412919898230240, 1122216138563359680, 69941868616009932480, 4675040053248335097600, 333605090142406849939200, 25312518953112479346316800

Offset: 0

Author

Seiichi Manyama, Sep 11 2023

Keywords

• nonn

Crossrefs

Cf. A347022, A365601, A365602, A365604.

Cf. A365587.

Programs

Mathematica

a[n_] := Sum[Product[5*j + 4, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)

PARI

a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+4)*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+4)) * Stirling1(n,k).

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