A376476 E.g.f. satisfies A(x) = exp( x^2*A(x)^2 * (1 + x*A(x)) ).
1, 0, 2, 6, 60, 720, 8400, 161280, 2857680, 66528000, 1650227040, 45984153600, 1430926136640, 47843446210560, 1760106348000000, 69273962466508800, 2936107841835168000, 132818888849994547200, 6387603066932383296000, 325931634111283200000000, 17558641895241269299276800
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*binomial(k, n-2*k)/k!);
Formula
E.g.f.: (1/x) * Series_Reversion( x*exp(-x^2 * (1 + x)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(k-1) * binomial(k,n-2*k)/k!.