A361214 E.g.f. satisfies A(x) = exp( 3*x*A(x) / (1+x) ).
1, 3, 21, 288, 5841, 158148, 5370003, 219641922, 10518990129, 577629889848, 35788733371179, 2470154920005798, 187970878034549001, 15636177199793409444, 1411635193678825868979, 137469669176542404342042, 14364540773583252035937633
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..338
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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Mathematica
Table[(-1)^n*n!*Sum[(-3)^k*(k + 1)^(k - 1)*Binomial[n - 1, n - k]/k!, {k, 0, n}], {n, 0, 20}] (* Wesley Ivan Hurt, May 25 2024 *) -
PARI
a(n) = (-1)^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) = (-1)^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)).