A362493 E.g.f. satisfies A(x) = exp(x - x^3/3 * A(x)^3).

1, 1, 1, -1, -31, -319, -2279, -4199, 269473, 7155233, 114846641, 920526641, -18415853279, -1115017249631, -31675298017271, -526379460621559, 2394778195929281, 603748739138745281, 27895091311964499553, 769764386129113157473, 6164705700089328588481

Offset: 0

Author

Seiichi Manyama, Apr 22 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362492, A362494.

Cf. A362478.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^3*exp(3*x))/3)))

Formula

E.g.f.: exp(x - LambertW(x^3 * exp(3*x))/3) = ( LambertW(x^3 * exp(3*x))/x^3 )^(1/3).

a(n) = n! * Sum_{k=0..floor(n/3)} (-1/3)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).