A365039 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)^2).

1, 1, -1, 7, -79, 1201, -22961, 530167, -14372191, 447825889, -15776617249, 620209389031, -26918670325295, 1278598424153233, -65973615445792081, 3674793950748867031, -219773335672937703871, 14046128883828030510529, -955409650156763223984449

Offset: 0

Author

Seiichi Manyama, Aug 18 2023

Keywords

• sign
• easy

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362771, A362773, A363478, A365038, A365040.

Cf. A361068.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(2*x*(1+x))/2)))

Formula

E.g.f.: exp( LambertW(2*x * (1+x))/2 ).

a(n) = n! * Sum_{k=0..n} (-2*k+1)^(k-1) * binomial(k,n-k)/k!.