A375627 Expansion of e.g.f. exp(2*x^2) / (1 - x * exp(x^2)).
1, 1, 6, 24, 168, 1260, 11760, 126000, 1545600, 21304080, 326350080, 5497873920, 101048048640, 2011924474560, 43139969832960, 991088998099200, 24286975237324800, 632358338278867200, 17433184834127462400, 507307459608530380800, 15539683835941532467200
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^2)/(1-x*exp(x^2)))) -
PARI
a(n) = n!*sum(k=0, n\2, (n-2*k+2)^k/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+2)^k/k!.