A365530 a(n) = Sum_{k=0..floor((n-2)/5)} Stirling2(n,5*k+2).

0, 0, 1, 3, 7, 15, 31, 64, 155, 717, 6391, 65010, 629444, 5719597, 49340838, 408864186, 3284672489, 25770192646, 198718943490, 1516391860879, 11554571944615, 89144035246500, 711587142257776, 6054854693784594, 56609279400922224, 590143167134961765

Offset: 0

Author

Seiichi Manyama, Sep 08 2023

Keywords

• nonn

Crossrefs

Cf. A365528, A365529, A365531, A365532.

Programs

PARI

a(n) = sum(k=0, (n-2)\5, stirling(n, 5*k+2, 2));

Formula

Let A(0)=1, B(0)=0, C(0)=0, D(0)=0 and E(0)=0. Let B(n+1) = Sum_{k=0..n} binomial(n,k)*A(k), C(n+1) = Sum_{k=0..n} binomial(n,k)*B(k), D(n+1) = Sum_{k=0..n} binomial(n,k)*C(k), E(n+1) = Sum_{k=0..n} binomial(n,k)*D(k) and A(n+1) = Sum_{k=0..n} binomial(n,k)*E(k). A365528(n) = A(n), A365529(n) = B(n), a(n) = C(n), A365531(n) = D(n) and A365532(n) = E(n).

G.f.: Sum_{k>=0} x^(5*k+2) / Product_{j=1..5*k+2} (1-j*x).