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A355290
a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling2(n,k) * Catalan(k).
1
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
0,5
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