A355290 a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling2(n,k) * Catalan(k).

1, 1, 1, 0, -3, -2, 23, 17, -333, 86, 6941, -17025, -160267, 1082864, 2273807, -56742606, 152154285, 2293098332, -22007462809, -15179437171, 1671107690083, -10716783889040, -58404948615167, 1439391012463810, -6701658223127029, -88340107011433060

Offset: 0

Author

Seiichi Manyama, Jun 27 2022

Keywords

• sign

Crossrefs

Cf. A000108, A006531, A064856, A086662, A086672.

Programs

Maple

A355290 := proc(n)
    add((-1)^(n-k)*stirling2(n,k)*A000108(k),k=0..n) ;
end proc:
seq(A355290(n),n=0..70) ; # R. J. Mathar, Mar 13 2023

PARI

a(n) = sum(k=0, n,(-1)^(n-k)*stirling(n, k, 2)*binomial(2*k, k)/(k+1));

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, binomial(2*k, k)/(k+1)*x^k/prod(j=1, k, 1+j*x)))

Formula

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