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A362276
a(n) = n! * Sum_{k=0..floor(n/2)} (-n/2)^k * binomial(n-k,k)/(n-k)!.
6
1, 1, -1, -8, 25, 326, -1709, -31016, 228257, 5311900, -50337449, -1429574464, 16573668409, 555724876552, -7619288730325, -294582728145824, 4662562423032961, 204200579987319824, -3664348770051277073, -179294278761195862400, 3597007651803106610201
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x - n*x^2/2).
E.g.f.: exp( sqrt( LambertW(x^2) ) ) / (1 + LambertW(x^2)).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(lambertw(x^2)))/(1+lambertw(x^2))))
CROSSREFS
Main diagonal of A362277.
Cf. A277614.
Sequence in context: A305680 A316927 A004246 * A220535 A060718 A060743
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 13 2023
STATUS
approved