A362654 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).

1, 1, 3, 22, 197, 2316, 33967, 595624, 12190761, 285479056, 7531645211, 221124649824, 7152276636397, 252742471065280, 9688895208298503, 400510408002257536, 17759663471017945553, 840937887639033467136, 42351198256293556043827

Offset: 0

Author

Seiichi Manyama, Apr 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A273954, A362655.

Cf. A362653, A362673.

Programs

PARI

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

Formula

E.g.f.: exp( -LambertW(-x * exp(x^2)) ).

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

a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n-1) * LambertW(2*exp(-2))^(n/2)). - Vaclav Kotesovec, Aug 05 2025