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A376563
E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x^3*A(x)^3) ).
1
1, 1, 3, 16, 149, 2016, 34447, 697264, 16349769, 438688000, 13302715931, 450127632384, 16805250091357, 685963808029696, 30389466219654375, 1452343581621354496, 74484586717220845073, 4080558161067766972416, 237830597688699873580339, 14694357436059217272832000
OFFSET
0,3
FORMULA
E.g.f.: (1/x) * Series_Reversion( x*exp(-x / (1 - x^3)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(n-3*k-1) * binomial(n-2*k-1,k)/(n-3*k)!.
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n+1)^(n-3*k-1)*binomial(n-2*k-1, k)/(n-3*k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 28 2024
STATUS
approved