A365526 a(n) = Sum_{k=0..floor((n-1)/4)} Stirling2(n,4*k+1).

0, 1, 1, 1, 1, 2, 16, 141, 1051, 6953, 42571, 247886, 1401676, 7868005, 45210257, 277899961, 1917140421, 15186484134, 135259346092, 1295096363273, 12821558136891, 128268683204737, 1283599391456735, 12817818177339530, 127998022119881272

Offset

0,6

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), a(n) = B(n), A365527(n) = C(n) and A099948(n) = D(n).

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

Mathematica

a[n_] := Sum[StirlingS2[n, 4*k+1], {k, 0, Floor[(n-1)/4]}]; Array[a, 25, 0] (* Amiram Eldar, Sep 13 2023 *)

Prog

(PARI) a(n) = sum(k=0, (n-1)\4, stirling(n, 4*k+1, 2));

Crossrefs

Cf. A099948, A365525, A365527.

Sequence in context: A056662 A348618 A151402 * A199565 A003768 A214767

Adjacent sequences: A365523 A365524 A365525 * A365527 A365528 A365529

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2023

Status

approved