A362525 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) / (6^k * k! * (n-3*k)!).
1, 1, 1, 2, 5, 11, 51, 246, 897, 7085, 51221, 260426, 2938541, 28279967, 184234415, 2714662406, 32614422401, 259026339161, 4721237878537, 67998862785970, 637019875964341, 13852253151455251, 232584488748665131, 2510358957337412182, 63466995535914172225
Offset: 0
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/6))))
Formula
E.g.f.: exp(x - LambertW(-x^3/6)) = -6 * LambertW(-x^3/6)/x^3 * exp(x).