A363529 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^4)).
1, 1, 3, 31, 409, 7361, 170251, 4732351, 154694961, 5814634753, 246946119571, 11698927124831, 611660759515081, 34984757221103041, 2173041881789331099, 145669007565799127551, 10482025117382045382241, 805892200757926620144641
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(-4*x^2*exp(4*x))/4)))
Formula
E.g.f.: exp( x - LambertW(-4*x^2*exp(4*x))/4 ).
a(n) = n! * Sum_{k=0..n} (4*n-4*k+1)^(k-1) * binomial(k,n-k)/k!.