A362691 E.g.f. satisfies A(x) = exp(x^3 + x * A(x)).
1, 1, 3, 22, 173, 1836, 24847, 403474, 7667865, 167097016, 4108985531, 112562882334, 3399748630357, 112246652293972, 4022094151907847, 155461592488721866, 6447531477912609713, 285606134199075271536, 13458367778796518816755
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^3-lambertw(-x*exp(x^3)))))
Formula
E.g.f.: -LambertW(-x * exp(x^3)) / x = exp( x^3 - LambertW(-x*exp(x^3)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).