A365040 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)^3).

1, 1, -3, 34, -623, 15636, -499277, 19382686, -886663647, 46716323752, -2786249779829, 185574001203834, -13652735530485647, 1099602989008154476, -96230900016000250269, 9092834662610587023286, -922622745817066477888703, 100054409045940667152740304

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, A365039.

Cf. A361069.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(3*x*(1+x))/3)))

Formula

E.g.f.: exp( LambertW(3*x * (1+x))/3 ).

a(n) = n! * Sum_{k=0..n} (-3*k+1)^(k-1) * binomial(k,n-k)/k!.