A362473 E.g.f. satisfies A(x) = exp(x + x^4 * A(x)^4).

1, 1, 1, 1, 25, 601, 9001, 105001, 1231441, 24146641, 740098801, 22443260401, 607394284201, 16102368745321, 497289446373721, 19072987370400601, 806135144596672801, 33945128330918599201, 1426006261391514829921, 63478993000497055809121

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A143768, A349562, A362472.

Cf. A362393, A362482, A362491.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-4*x^4*exp(4*x))/4)))

Formula

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

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