A362661 E.g.f. satisfies A(x) = exp( x * exp(x^3/6) * A(x) ).
1, 1, 3, 16, 129, 1356, 17767, 279714, 5149209, 108591688, 2582351451, 68380940904, 1995777685717, 63659665732716, 2203395556479951, 82253291389678756, 3294326092613575473, 140911264444599281616, 6411278790217738946899
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*exp(x^3/6)))))
Formula
E.g.f.: exp( -LambertW(-x * exp(x^3/6)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^k * (n-3*k+1)^(n-3*k-1) / (6^k * k! * (n-3*k)!).