A378042 - OEIS

A378042

E.g.f. satisfies A(x) = exp( x * A(x)^3 / (1-x) ) / (1-x).

1, 2, 19, 385, 12041, 512101, 27616705, 1806241151, 138948411649, 12294333869545, 1230146587626041, 137347201671983227, 16928938651265737585, 2283232081600363345037, 334480117852142180147377, 52888942867094899879009111, 8978241760087200983202588545, 1628601738501672908949881316433

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

E.g.f.: exp( -LambertW(-3*x/(1-x)^4)/3 )/(1-x).

a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n+3*k,n-k)/k!.

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1-x)^4)/3)/(1-x)))

(PARI) a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(n+3*k, n-k)/k!);