A375634 Expansion of e.g.f. exp(x^3) / (1 - x * exp(x^3/6)).
1, 1, 2, 12, 52, 280, 2160, 16870, 150080, 1557360, 17491600, 215908000, 2923905600, 42734091400, 672515043200, 11347480544400, 204142655516800, 3902009862150400, 78976503077472000, 1687212801048174400, 37941749192547200000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x*exp(x^3/6)))) -
PARI
a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k/k!.