A365588 Expansion of e.g.f. 1 / (1 + 5 * log(1-x)).

1, 5, 55, 910, 20080, 553870, 18333050, 707959800, 31244562600, 1551289408800, 85579293493200, 5193226343508000, 343790892166398000, 24655487205067386000, 1904221630155352038000, 157574022827034258192000, 13908505761692419540320000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..350

Formula

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

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

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (5 * exp(4*n/5) * (exp(1/5) - 1)^(n+1)). - Vaclav Kotesovec, Nov 11 2023

Mathematica

a[n_] := Sum[5^k * k! * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)

Prog

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

Crossrefs

Column k=5 of A320079.

Cf. A346987, A365585, A365586, A365587.

Cf. A094418.

Sequence in context: A145662 A362653 A094418 * A367164 A008543 A057130

Adjacent sequences: A365585 A365586 A365587 * A365589 A365590 A365591

Keyword

nonn

Author

Seiichi Manyama, Sep 10 2023

Status

approved