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%I #12 Apr 22 2023 10:32:59
%S 1,1,1,1,25,601,9001,105001,1231441,24146641,740098801,22443260401,
%T 607394284201,16102368745321,497289446373721,19072987370400601,
%U 806135144596672801,33945128330918599201,1426006261391514829921,63478993000497055809121
%N E.g.f. satisfies A(x) = exp(x + x^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(-4*x^4 * exp(4*x))/4) = ( -LambertW(-4*x^4 * exp(4*x))/(4*x^4) )^(1/4).
%F a(n) = n! * Sum_{k=0..floor(n/4)} (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-4*x^4*exp(4*x))/4)))
%Y Cf. A143768, A349562, A362472.
%Y Cf. A362393, A362482, A362491.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Apr 21 2023
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