A372159 E.g.f. A(x) satisfies A(x) = exp( 3 * x * A(x)^(1/3) / (1 - x) ).
1, 3, 21, 216, 2937, 49788, 1013247, 24106134, 657277185, 20225122632, 693755934159, 26261393088978, 1087866116802081, 48965716033901436, 2380245527593532559, 124300353332797939422, 6941285402232405794817, 412817223292008085699344
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(-3*lambertw(-x/(1-x))))) -
PARI
a(n, r=3, s=1, t=1, u=0) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
Formula
E.g.f.: A(x) = exp( -3 * LambertW(-x / (1-x)) ).
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.