A355290 - OEIS

%I #15 Mar 13 2023 15:53:06

%S 1,1,1,0,-3,-2,23,17,-333,86,6941,-17025,-160267,1082864,2273807,

%T -56742606,152154285,2293098332,-22007462809,-15179437171,

%U 1671107690083,-10716783889040,-58404948615167,1439391012463810,-6701658223127029,-88340107011433060

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

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

%p A355290 := proc(n)

%p     add((-1)^(n-k)*stirling2(n,k)*A000108(k),k=0..n) ;

%p end proc:

%p seq(A355290(n),n=0..70) ; # _R. J. Mathar_, Mar 13 2023

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

%o (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)))

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

%K sign

%O 0,5

%A _Seiichi Manyama_, Jun 27 2022