A365531 a(n) = Sum_{k=0..floor((n-3)/5)} Stirling2(n,5*k+3).

0, 0, 0, 1, 6, 25, 90, 301, 967, 3061, 10080, 40381, 245553, 2161238, 21701381, 219007491, 2149071359, 20442363031, 189226358659, 1712836890912, 15232581945180, 133717667932475, 1164901223314180, 10143255631462661, 89207257764369032, 804712211338739040

Offset

0,5

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), 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).

Prog

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

Crossrefs

Cf. A365528, A365529, A365530, A365532.

Sequence in context: A309946 A001871 A000392 * A099948 A333017 A277973

Adjacent sequences: A365528 A365529 A365530 * A365532 A365533 A365534

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2023

Status

approved