A365055 E.g.f. satisfies A(x) = exp( x * (1+x/2) * A(x)^3 ).
1, 1, 8, 121, 2818, 89006, 3559504, 172489948, 9825889532, 643567980808, 47654835126436, 3936868360416476, 358990055621209984, 35816155847478234424, 3880967272702222156952, 453886307361640406266456, 56985342864303337121933584, 7644651551838264804179619200
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..331
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x*(1+x/2))/3)))
Formula
E.g.f.: exp( -LambertW(-3*x * (1+x/2))/3 ).
a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (3*k+1)^(k-1) * binomial(k,n-k)/k!.