0,4

Let A(0)=1, B(0)=0, C(0)=0 and D(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) and A(n+1) = Sum_{k=0..n} binomial(n,k)*D(k). A365525(n) = A(n), A365526(n) = B(n), a(n) = C(n) and A099948(n) = D(n).

G.f.: Sum_{k>=0} x^(4*k+2) / Product_{j=1..4*k+2} (1-j*x).

a[n_] := Sum[StirlingS2[n, 4*k+2], {k, 0, Floor[(n-2)/4]}]; Array[a, 25, 0] (* Amiram Eldar, Sep 13 2023 *)

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

Cf. A099948, A365525, A365526.

Sequence in context: A101890 A307573 A134195 * A079444 A269560 A146654

Adjacent sequences: A365524 A365525 A365526 * A365528 A365529 A365530

Seiichi Manyama, Sep 08 2023

approved