A376558 E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x^2*A(x)^2) ).
1, 1, 3, 22, 245, 3576, 65527, 1449904, 37596393, 1118442880, 37559084651, 1405597826304, 58012540741597, 2617923512200192, 128240561732097375, 6777245042104293376, 384358793388984148433, 23284761629109883600896, 1500714780345430134323923
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*binomial(n-k-1, k)/(n-2*k)!);
Formula
E.g.f.: (1/x) * Series_Reversion( x*exp(-x / (1 - x^2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * binomial(n-k-1,k)/(n-2*k)!.