A362494 E.g.f. satisfies A(x) = exp(x - x^4/4 * A(x)^4).

1, 1, 1, 1, -5, -149, -2249, -26249, -251159, -1443959, 21646801, 1209344401, 35457894451, 817789456771, 14796993881671, 137893562065351, -4661597156689199, -372730180154530799, -16419790692323174879, -559989133713039523679, -14492546886670841884949

Offset: 0

Author

Seiichi Manyama, Apr 22 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362492, A362493.

Cf. A362491.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^4*exp(4*x))/4)))

Formula

E.g.f.: exp(x - LambertW(x^4 * exp(4*x))/4) = ( LambertW(x^4 * exp(4*x))/x^4 )^(1/4).

a(n) = n! * Sum_{k=0..floor(n/4)} (-1/4)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).