A362282 a(n) = n! * Sum_{k=0..floor(n/2)} (-n)^k * binomial(n-k,k)/(n-k)!.

1, 1, -3, -17, 145, 1401, -19619, -267833, 5214273, 91975825, -2292948899, -49586832129, 1506939887377, 38595456391753, -1383612408628995, -40951481342092649, 1691614670048805121, 56809502720559644577, -2656760323700732460227, -99810124102484722532465

Offset: 0

Author

Seiichi Manyama, Apr 14 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..394
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362276, A362277, A362281.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(lambertw(2*x^2)/2))/(1+lambertw(2*x^2))))

Formula

a(n) = A362277(n,2*n).

a(n) = n! * [x^n] exp(x - n*x^2).

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