|
%I #14 Feb 17 2023 15:02:45
%S 0,1,6,63,1044,23805,692118,24482115,1020584232,49000005945,
%T 2662853279850,161586078510879,10830019921469532,794577001293803637,
%U 63339899145968483262,5451312770064188283195,503784284643602483767632,49757423537114340032969073
%N E.g.f. satisfies A(x) = x * exp(x + 2 * A(x)).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: A(x) = -LambertW(-2*x * exp(x))/2.
%F a(n) = Sum_{k=1..n} 2^(k-1) * k^(n-1) * binomial(n,k).
%F a(n) ~ sqrt(1 + LambertW(exp(-1)/2)) * n^(n-1) / (2 * LambertW(exp(-1)/2)^n * exp(n)). - _Vaclav Kotesovec_, Feb 17 2023
%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x*exp(x))/2)))
%o (PARI) a(n) = sum(k=1, n, 2^(k-1)*k^(n-1)*binomial(n, k));
%Y Cf. A216857, A360482, A360483, A360484.
%Y Cf. A360473.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 09 2023
|
