A365602 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(3/5).

1, 3, 21, 246, 3990, 82800, 2092560, 62343600, 2139137760, 83064002160, 3600715721040, 172353630085920, 9028586395211040, 513740204261763840, 31553316959017737600, 2080500578006553619200, 146577866381052082876800, 10988979300484733769667200

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * Stirling1(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k).

Mathematica

a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 1));

Crossrefs

Cf. A347022, A365601, A365603, A365604.

Cf. A365586.

Sequence in context: A138213 A193333 A290129 * A371006 A355092 A205319

Adjacent sequences: A365599 A365600 A365601 * A365603 A365604 A365605

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2023

Status

approved