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%I #13 Mar 10 2024 09:06:27
%S 1,1,0,6,48,180,2880,46200,483840,9087120,203212800,3752511840,
%T 89413632000,2510276408640,66301996400640,1982685238934400,
%U 67064515854336000,2274167610024710400,82881756045036748800,3301346557970183923200,135363022243685203968000
%N E.g.f. satisfies A(x) = 1 + x*exp(x^2*A(x)^2).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(2*k+1,n-2*k)/( (2*k+1)*k! ).
%F 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
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(2*k+1, n-2*k)/((2*k+1)*k!));
%Y Cf. A365283, A370927.
%Y Cf. A161631, A371068.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Mar 09 2024
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