A365057 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x/2 * A(x)^2)).
1, 1, 6, 70, 1242, 29766, 901108, 33007500, 1419955260, 70189326748, 3920638941576, 244244850932424, 16790688671875000, 1262666306235233160, 103110586277262570672, 9086730135842989237456, 859557307380692050631952, 86872483166310571406250000
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Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (1/2)^(n-k)*(2*n+1)^(k-1)*binomial(k, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (2*n+1)^(k-1) * binomial(k,n-k)/k!.