A365527 a(n) = Sum_{k=0..floor((n-2)/4)} Stirling2(n,4*k+2).

0, 0, 1, 3, 7, 15, 32, 84, 393, 2901, 23339, 180565, 1327404, 9364732, 64197317, 433372411, 2928720335, 20264399483, 147807954692, 1170622475408, 10229966924581, 97922117830589, 1001744359476291, 10661002700183905, 115706501336004984

Offset

0,4

Links

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

Formula

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A099948, A365525, A365526.

Sequence in context: A101890 A307573 A134195 * A079444 A269560 A146654

Adjacent sequences: A365524 A365525 A365526 * A365528 A365529 A365530

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2023

Status

approved