A363354 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^3)).
1, 1, 3, 25, 277, 4221, 81421, 1891429, 51638217, 1618907257, 57332786041, 2264047223241, 98641443498973, 4700569138096885, 243213757144477029, 13579261873673960941, 813757288951509415441, 52098716516012891238129, 3548972379593741013388657
Offset: 0
Keywords
Links
- 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(x-lambertw(-3*x^2*exp(3*x))/3)))
Formula
E.g.f.: exp( x - LambertW(-3*x^2*exp(3*x))/3 ).
a(n) = n! * Sum_{k=0..n} (3*n-3*k+1)^(k-1) * binomial(k,n-k)/k!.