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

Author

Seiichi Manyama, Oct 20 2022

Keywords

• sign

Crossrefs

Cf. A357901, A357920.

Programs

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

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)))

Formula

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