A376093 E.g.f. A(x) satisfies A(x) = x * exp(2*A(x)) * (1 + A(x)).
0, 1, 6, 78, 1592, 44520, 1584432, 68531344, 3491058048, 204734169216, 13586332140800, 1006537369922304, 82349234930543616, 7374284286510988288, 717422903095894775808, 75349693916700334848000, 8497322752297075356827648, 1024074762391754154176446464
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Keywords
Programs
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PARI
a(n) = n!*sum(k=1, n, (2*n)^(k-1)*binomial(n-1, k-1)/k!);
Formula
E.g.f.: Series_Reversion( x * exp(-2*x) / (1 + x) ).
a(n) = n! * Sum_{k=1..n} (2*n)^(k-1) * binomial(n-1,k-1)/k!.
a(n) ~ n^(n-1) / (2 * 3^(1/4) * (2 - sqrt(3))^n * exp((2 - sqrt(3))*n)). - Vaclav Kotesovec, Sep 10 2024