A362571 - OEIS

%I #19 May 04 2023 09:52:51

%S 1,1,1,1,25,121,361,8401,82321,456625,11496241,172149121,1452983401,

%T 40947003241,823437038425,9491714865361,300842942443681,

%U 7568303382376801,111494036396244961,3957438528527140225,119206427681076135481,2147109997071581380441

%N E.g.f. satisfies A(x) = exp(x * A(x)^(x^2)).

%H Seiichi Manyama, <a href="/A362571/b362571.txt">Table of n, a(n) for n = 0..427</a>

%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(-x^3) / x^3)^(1/x^2) = exp(-LambertW(-x^3) / x^2) = exp(x * exp(-LambertW(-x^3))).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-2*k)^k * binomial(n-2*k-1,k)/(n-2*k)!.

%F E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * x^k / k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^3)))))

%Y Cf. A000272, A361777.

%Y Cf. A362569, A362573.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Apr 25 2023