A360596 Expansion of e.g.f. 1/( (1 - x) * (1 + LambertW(-2*x)) ).
1, 3, 22, 282, 5224, 126120, 3742704, 131612432, 5347866752, 246490091136, 12704900911360, 724072211436288, 45209213973292032, 3068872654856532992, 225023336997933996032, 17724257054969009940480, 1492513932494133333753856, 133800772458366199028023296
Offset: 0
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(1/((1-x)*(1+lambertw(-2*x))))) -
PARI
a(n) = n!*sum(k=0, n, (2*k)^k/k!);
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+(2*i)^i); v;
Formula
a(n) = n! * Sum_{k=0..n} (2*k)^k / k!.
a(0)=1; a(n) = n*a(n-1) + (2*n)^n.
a(n) ~ 2^(n+1) * n^n / (2 - exp(-1)). - Vaclav Kotesovec, Feb 13 2023