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%I #11 Apr 22 2023 10:32:40
%S 1,1,1,1,-5,-149,-2249,-26249,-251159,-1443959,21646801,1209344401,
%T 35457894451,817789456771,14796993881671,137893562065351,
%U -4661597156689199,-372730180154530799,-16419790692323174879,-559989133713039523679,-14492546886670841884949
%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. A362492, A362493.
%Y Cf. A362491.
%K sign
%O 0,5
%A _Seiichi Manyama_, Apr 22 2023
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