%I #16 Apr 29 2023 08:40:13
%S 1,1,3,22,197,2316,33967,595624,12190761,285479056,7531645211,
%T 221124649824,7152276636397,252742471065280,9688895208298503,
%U 400510408002257536,17759663471017945553,840937887639033467136,42351198256293556043827
%N E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp( -LambertW(-x * exp(x^2)) ).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (n-2*k+1)^(n-2*k-1) / (k! * (n-2*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*exp(x^2)))))
%Y Cf. A273954, A362655.
%Y Cf. A362653, A362673.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 28 2023