A353288 a(n) = Sum_{k=0..floor(n/2)} k^(n-2*k) * Stirling2(n-k,k).
1, 0, 1, 1, 2, 7, 30, 139, 723, 4487, 33551, 289854, 2774999, 29016343, 333139222, 4232908176, 59442337179, 912948755487, 15154215501815, 269933506466203, 5150440487875190, 105326085645729766, 2307425141636199329, 53998118146846356916, 1343998910355295080556
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/prod(j=1, k, 1-k*j*x))) -
PARI
a(n) = sum(k=0, n\2, k^(n-2*k)*stirling(n-k, k, 2));
Formula
G.f.: Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - k * j * x).