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

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..394

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

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)).

Prog

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

Crossrefs

Cf. A362276, A362277, A362281.

Sequence in context: A333331 A198860 A298691 * A051442 A368236 A162650

Adjacent sequences: A362279 A362280 A362281 * A362283 A362284 A362285

Keyword

sign

Author

Seiichi Manyama, Apr 14 2023

Status

approved