A365529 a(n) = Sum_{k=0..floor((n-1)/5)} Stirling2(n,5*k+1).

0, 1, 1, 1, 1, 1, 2, 22, 267, 2647, 22828, 179489, 1323719, 9323744, 63502440, 422172752, 2763863468, 18017811013, 119078265944, 822495346707, 6206943675825, 53413341096271, 529613886789747, 5863983528090106, 69211078916780252, 839908976768680556

Offset

0,7

Links

Table of n, a(n) for n=0..25.

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), a(n) = B(n), A365530(n) = C(n), A365531(n) = D(n) and A365532(n) = E(n).

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

Prog

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

Crossrefs

Cf. A365528, A365530, A365531, A365532.

Sequence in context: A226706 A036841 A307852 * A264836 A135634 A156505

Adjacent sequences: A365526 A365527 A365528 * A365530 A365531 A365532

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2023

Status

approved