0,5

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), a(n) = D(n) and A365532(n) = E(n).

G.f.: Sum_{k>=0} x^(5*k+3) / Product_{j=1..5*k+3} (1-j*x).

(PARI) a(n) = sum(k=0, (n-3)\5, stirling(n, 5*k+3, 2));

Cf. A365528, A365529, A365530, A365532.

Sequence in context: A384506 A001871 A000392 * A099948 A333017 A277973

Adjacent sequences: A365528 A365529 A365530 * A365532 A365533 A365534

Seiichi Manyama, Sep 08 2023

approved