A361212 E.g.f. satisfies A(x) = exp( 3*x*A(x) / (1-x) ).
1, 3, 33, 612, 16353, 576108, 25306803, 1334701854, 82258866225, 5805344935368, 461848917299499, 40904277651802458, 3992219566916292873, 425766991650939828828, 49266876888419716251315, 6147944525591645916094182, 823045511075200872642258273
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..327
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
a(n) = n!*sum(k=0, n, 3^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1-x))))) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)/(3*x)*lambertw(-3*x/(1-x))))
Formula
a(n) = n! * Sum_{k=0..n} 3^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
E.g.f.: exp ( -LambertW(-3*x/(1-x)) ).
E.g.f.: -(1-x)/(3*x) * LambertW(-3*x/(1-x)).