A375587 Expansion of e.g.f. 1 / (1 + x - x * exp(x^3/6)).
1, 0, 0, 0, 4, 0, 0, 70, 1120, 0, 2800, 184800, 2217600, 200200, 39239200, 1513512000, 16166550400, 11435424000, 1029188160000, 31290941281600, 317363510464000, 821292151680000, 52198475641312000, 1387554839326656000, 14092570281613824000, 92349968764253200000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^3/6)))) -
PARI
a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/(6^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * Stirling2(k,n-3*k)/(6^k*k!).