A371067 E.g.f. satisfies A(x) = 1 + x*exp(x^2*A(x)^2).
1, 1, 0, 6, 48, 180, 2880, 46200, 483840, 9087120, 203212800, 3752511840, 89413632000, 2510276408640, 66301996400640, 1982685238934400, 67064515854336000, 2274167610024710400, 82881756045036748800, 3301346557970183923200, 135363022243685203968000
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(2*k+1, n-2*k)/((2*k+1)*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(2*k+1,n-2*k)/( (2*k+1)*k! ).
a(n) ~ n^(n-1) / (sqrt(2) * exp(n) * r^(n+1)), where r = 0.450347181930267755599214125867779338412791581819135528888185619948594... and s = 2.1478259175343697310213089706837271102656629945040966643073615920885... are roots of the system of equations exp(r^2*s^2)*r = s-1, 2*(s-1)*r^2*s = 1. - Vaclav Kotesovec, Mar 10 2024