A365568 Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(2/5).

1, 2, 16, 212, 3964, 95804, 2840140, 99760124, 4050900268, 186700658972, 9628444876108, 549349531209404, 34355463031007596, 2336935606239856988, 171779270567736231052, 13568895740353218626300, 1146225546710339427328684, 103113032296428007394503580

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+2)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (5 - 3*k/n) * binomial(n,k) * a(n-k).

a(n) ~ sqrt(Pi) * 2^(1/10) * n^(n - 1/10) / (3^(2/5) * Gamma(2/5) * exp(n) * log(6/5)^(n + 2/5)). - Vaclav Kotesovec, Nov 11 2023

a(0) = 1; a(n) = 2*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 + 2, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 11 2023 *)

Prog

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

Crossrefs

Cf. A094418, A346984, A365569, A365570.

Sequence in context: A206865 A349313 A364399 * A360939 A114531 A365585

Adjacent sequences: A365565 A365566 A365567 * A365569 A365570 A365571

Keyword

nonn

Author

Seiichi Manyama, Sep 09 2023

Status

approved