%I #12 Apr 14 2023 13:47:13
%S 1,1,1,4,13,106,601,7456,60649,1012348,10748161,225641296,2957978101,
%T 74847384184,1168123938073,34598428916416,626497273410961,
%U 21261683280971536,438222313050326209,16765636110497697088,387549609831150094621,16502188154766906299296
%N Expansion of e.g.f. exp( sqrt(-LambertW(-x^2)) ).
%H Seiichi Manyama, <a href="/A362283/b362283.txt">Table of n, a(n) for n = 0..417</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} A034940(k) * binomial(n-1,2*k) * a(n-2*k-1).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(-lambertw(-x^2)))))
%Y Cf. A000272, A034940, A277614, A362293.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 14 2023