A376477 E.g.f. satisfies A(x) = exp( x^3*A(x)^3 * (1 + x*A(x)) ).
1, 0, 0, 6, 24, 0, 2520, 40320, 181440, 6048000, 219542400, 2874009600, 57340483200, 2847824179200, 73556683200000, 1606870263398400, 77095250039808000, 3111553620983808000, 91548244100875161600, 4054836680294400000000, 210947475222439667712000, 8463340108487290650624000, 381818416967499733917696000
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\3, (n+1)^(k-1)*binomial(k, n-3*k)/k!);
Formula
E.g.f.: (1/x) * Series_Reversion( x*exp(-x^3 * (1 + x)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(k-1) * binomial(k,n-3*k)/k!.