A365570 Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(4/5).

1, 4, 40, 616, 12856, 338728, 10781176, 402250216, 17213590840, 831013114792, 44675458306168, 2646758624166760, 171319908334752184, 12028779733435667752, 910538645035885918456, 73918475291961325824232, 6406179168820339231897144

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+4)) * Stirling2(n,k).

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

a(n) ~ sqrt(2*Pi) * n^(n + 3/10) / (6^(4/5) * Gamma(4/5) * exp(n) * log(6/5)^(n + 4/5)). - Vaclav Kotesovec, Nov 11 2023

a(0) = 1; a(n) = 4*a(n-1) - 6*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Nov 16 2023

Mathematica

a[n_] := Sum[Product[5*j + 4, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 11 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+4)*stirling(n, k, 2));

Crossrefs

Cf. A094418, A346984, A365568, A365569.

Sequence in context: A052675 A141010 A141011 * A365587 A090359 A049308

Adjacent sequences: A365567 A365568 A365569 * A365571 A365572 A365573

Keyword

nonn

Author

Seiichi Manyama, Sep 09 2023

Status

approved