%I #13 Apr 23 2023 02:06:42

%S 1,1,4,28,298,4186,74116,1578340,39394972,1127378332,36411516496,

%T 1310173698736,51982859674648,2254757407407064,106150698182657584,

%U 5390926011965379376,293782337188718257936,17100576708082841577232,1058920120014192744673600

%N E.g.f. satisfies A(x) = exp(x + 3*x^2/2 * A(x)^2).

%H Seiichi Manyama, <a href="/A362475/b362475.txt">Table of n, a(n) for n = 0..370</a>

%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(x - LambertW(-3*x^2 * exp(2*x))/2) = sqrt( -LambertW(-3*x^2 * exp(2*x))/(3*x^2) ).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (3/2)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^2*exp(2*x))/2)))

%Y Column k=3 of A362483.

%Y Cf. A143768, A362474.

%Y Cf. A362380.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 21 2023