|
%I #14 Mar 09 2024 08:16:01
%S 1,1,4,24,228,2820,44400,840000,18669840,475871760,13698296640,
%T 439402803840,15545690233920,601352177025600,25251437978807040,
%U 1143932660001331200,55612090342967558400,2887929114414030086400,159548423949650274739200
%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^2)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(n,2*k)/k!.
%F E.g.f.: sqrt(LambertW( -2*x^2/(1-x)^2 ) / (-2*x^2)).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^2)))/x))
%o (PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n, 2*k)/k!);
%Y Cf. A352410, A370876.
%Y Cf. A360601.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 03 2024
|
