A357919 a(n) = Sum_{k=0..floor(n/3)} Stirling1(n - 2*k,k).

1, 0, 0, 1, -1, 2, -5, 21, -109, 671, -4772, 38591, -350036, 3520830, -38903271, 468490350, -6107642906, 85704534787, -1288021805215, 20641247413120, -351374756822383, 6332030169529731, -120427840368046909, 2410627702030000447, -50661193580285096086

Offset

0,6

Links

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

Formula

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

Maple

A357919 := proc(n)
    add(stirling1(n-2*k, k), k=0..n/3) ;
end proc:
seq(A357919(n), n=0..70) ; # R. J. Mathar, Mar 13 2023

Prog

(PARI) a(n) = sum(k=0, n\3, stirling(n-2*k, k, 1));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k*prod(j=0, k-1, j-x^2)))

Crossrefs

Cf. A357901, A357920.

Sequence in context: A130471 A002628 A370656 * A020129 A129582 A152576

Adjacent sequences: A357916 A357917 A357918 * A357920 A357921 A357922

Keyword

sign

Author

Seiichi Manyama, Oct 20 2022

Status

approved