The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #11 Apr 20 2023 09:03:07
%S 1,1,0,-5,-14,56,736,1114,-45156,-428660,2004796,82797716,446153632,
%T -13593781928,-276074700264,701782138576,107474258830096,
%U 1263010302870608,-30208216250914352,-1146149464640506928,-2087509382334856224,703335832718961413056
%N E.g.f. satisfies A(x) = exp(x - x^2/2 * A(x)).
%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(x - LambertW(x^2/2 * exp(x))) = 2 * LambertW(x^2/2 * exp(x))/x^2.
%F a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2/2*exp(x)))))
%Y Column k=1 of A362394.
%Y Cf. A143740.
%K sign
%O 0,4
%A _Seiichi Manyama_, Apr 20 2023