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%I #12 Apr 22 2023 10:26:35
%S 1,1,1,1,7,151,2251,26251,273841,3281041,61021801,1518719401,
%T 38199828151,905801252071,21398411003971,560160675014851,
%U 17260034904184801,596005144436100001,21359751419836426321,773082506262449261521,28839945213850125032551
%N E.g.f. satisfies A(x) = exp(x + x^4/4 * A(x)^4).
%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(-x^4 * exp(4*x))/4) = ( -LambertW(-x^4 * exp(4*x))/x^4 )^(1/4).
%F a(n) = n! * Sum_{k=0..floor(n/4)} (1/4)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^4*exp(4*x))/4)))
%Y Cf. A362474, A362478.
%Y Cf. A362473, A362494.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Apr 22 2023
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