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A375589
Expansion of e.g.f. 1 / (1 + x - x * exp(x^3)).
2
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 604800, 39916800, 479001600, 259459200, 50854003200, 1961511552000, 21097146470400, 88921857024000, 8002967132160000, 243459152346009600, 2642401903325184000, 38318206628782080000, 2435557926202232832000
OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * Stirling2(k,n-3*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^3))))
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 19 2024
STATUS
approved