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A308506 Expansion of e.g.f.: -1/(1-LambertW(-2*x)).

%I A308506 #16 Apr 13 2020 06:00:26
%S A308506 -1,2,0,24,256,5280,129024,3893120,138215424,5657154048,262183321600,
%T A308506 13572739749888,776265384591360,48609716407476224,3307818108252585984,
%U A308506 243052603284860928000,19179014510218162733056,1617564760662882792898560,145212699111541646687207424
%N A308506 Expansion of e.g.f.: -1/(1-LambertW(-2*x)).
%H A308506 Robert Israel, <a href="/A308506/b308506.txt">Table of n, a(n) for n = 0..351</a>
%F A308506 a(n) ~ 2^(n-2) * n^(n-1).
%p A308506 de:= diff(y(x),x) = x*y(x)^3/(1-2*x*y(x)):
%p A308506 S:= rhs(dsolve({de, y(0)=2},y(x), series, order=40)):
%p A308506 -1, seq(coeff(S,x,i)*(i+1)!,i=0..39); # _Robert Israel_, Apr 13 2020
%t A308506 CoefficientList[Series[-1/(1-LambertW[-2*x]), {x, 0, 20}], x] * Range[0, 20]!
%o A308506 (PARI) my(x='x+O('x^20)); Vec(serlaplace(-1/(1-lambertw(-2*x)))) \\ _Michel Marcus_, Apr 13 2020
%Y A308506 Cf. A000312, A062971, A277458.
%K A308506 sign
%O A308506 0,2
%A A308506 _Vaclav Kotesovec_, Jun 02 2019