A362653 - OEIS

%I #12 Apr 29 2023 09:09:30

%S 1,1,5,55,849,17641,462373,14651295,545025281,23291218801,

%T 1124589371301,60553038168679,3597677815336465,233810179507710105,

%U 16499939198003013509,1256544674435523638671,102713141497515307408257,8970278754666722087785825

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

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

%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-4*k+1)^(n-2*k-1) / (k! * (n-2*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*exp(x^2))/2)))

%Y Cf. A360547, A362654, A362673.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 28 2023