%I #10 Mar 09 2024 08:16:11
%S 1,1,4,30,348,5460,108480,2609040,73713360,2393087760,87791891040,
%T 3591843726240,162157925160000,8007919490450880,429418816003457280,
%U 24849579630222547200,1543505958412498080000,102430107277414595078400,7232759636684706937612800
%N E.g.f. satisfies A(x) = exp(x^2*A(x)^3) / (1-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.: (LambertW( -3*x^2/(1-x)^3 ) / (-3*x^2))^(1/3).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (3*k+1)^(k-1) * binomial(n+k,n-2*k)/k!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x^2/(1-x)^3)/(-3*x^2))^(1/3)))
%o (PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*binomial(n+k, n-2*k)/k!);
%Y Cf. A360609, A370876.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 09 2024
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