OFFSET
0,5
FORMULA
G.f.: Sum_{k>=0} Catalan(k) * x^k / Product_{j=1..k} (1 + j*x).
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
PROG
(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)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 27 2022
STATUS
approved