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A356796 E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^3).

%I A356796 #24 Feb 16 2025 08:34:03
%S A356796 1,0,2,3,92,450,14454,141540,4980128,78711696,3048567480,68677353360,
%T A356796 2930551701384,86832573553440,4079649847428960,150444517302424800,
%U A356796 7768028697749806080,342721736137376184960,19392702029822685015360,994397473912386435004800
%N A356796 E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^3).
%H A356796 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A356796 a(n) = n! * Sum_{k=0..floor(n/2)} (3*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!.
%F A356796 E.g.f.: A(x) = Sum_{k>=0} (3*k+1)^(k-1) * (-x * log(1-x))^k / k!.
%F A356796 E.g.f.: A(x) = exp( -LambertW(3 * x * log(1-x))/3 ).
%F A356796 E.g.f.: A(x) = ( LambertW(3 * x * log(1-x))/(3 * x * log(1-x)) )^(1/3).
%o A356796 (PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
%o A356796 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k+1)^(k-1)*(-x*log(1-x))^k/k!)))
%o A356796 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(3*x*log(1-x))/3)))
%o A356796 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(3*x*log(1-x))/(3*x*log(1-x)))^(1/3)))
%Y A356796 Cf. A066166, A355842, A356795.
%Y A356796 Cf. A356787.
%K A356796 nonn
%O A356796 0,3
%A A356796 _Seiichi Manyama_, Aug 28 2022