A362337 a(n) = n! * Sum_{k=0..floor(n/2)} (-k)^k / (k! * (n-2*k)!).

1, 1, -1, -5, 37, 221, -2549, -21041, 342665, 3604537, -75816809, -970017949, 25012223149, 377031935125, -11513789879773, -199833956857289, 7052339905578001, 138505710577529969, -5546345926322582225, -121599560980889072693, 5447342134797972438581

Offset: 0

Author

Seiichi Manyama, Apr 17 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A069856, A362338, A362339.

Cf. A362347.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^2))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^2)).