A365532 a(n) = Sum_{k=0..floor((n-4)/5)} Stirling2(n,5*k+4).

0, 0, 0, 0, 1, 10, 65, 350, 1701, 7771, 34150, 146905, 633776, 2892032, 15526876, 109484545, 992589171, 10223409493, 108982611518, 1156117871286, 12062817285396, 123603289559039, 1245986248828926, 12391614409960544, 121996350285087172

Offset

0,6

Links

Table of n, a(n) for n=0..24.

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), A365530(n) = C(n), A365531(n) = D(n) and a(n) = E(n).

G.f.: Sum_{k>=0} x^(5*k+4) / Product_{j=1..5*k+4} (1-j*x).

Prog

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

Crossrefs

Cf. A365528, A365529, A365530, A365531.

Sequence in context: A003519 A056280 A000453 * A365525 A327505 A346954

Adjacent sequences: A365529 A365530 A365531 * A365533 A365534 A365535

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2023

Status

approved