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

-1, 2, 0, 24, 256, 5280, 129024, 3893120, 138215424, 5657154048, 262183321600, 13572739749888, 776265384591360, 48609716407476224, 3307818108252585984, 243052603284860928000, 19179014510218162733056, 1617564760662882792898560, 145212699111541646687207424

Offset: 0

Author

Vaclav Kotesovec, Jun 02 2019

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..351

Crossrefs

Cf. A000312, A062971, A277458.

Programs

Maple

de:= diff(y(x),x) = x*y(x)^3/(1-2*x*y(x)):
S:= rhs(dsolve({de, y(0)=2},y(x), series, order=40)):
-1, seq(coeff(S,x,i)*(i+1)!,i=0..39); # Robert Israel, Apr 13 2020

Mathematica

CoefficientList[Series[-1/(1-LambertW[-2*x]), {x, 0, 20}], x] * Range[0, 20]!

PARI

my(x='x+O('x^20)); Vec(serlaplace(-1/(1-lambertw(-2*x)))) \\ Michel Marcus, Apr 13 2020

Formula

a(n) ~ 2^(n-2) * n^(n-1).