A357336 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(3 * A(x)).
0, 1, 7, 100, 2257, 70021, 2768740, 133164109, 7546722487, 492531820066, 36381833190223, 3000677194970137, 273342303933512362, 27256107730344331879, 2952882035628632383975, 345384835617231362018764, 43378466647737203462409829, 5822506028894124326533926193
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
- Index entries for reversions of series
Programs
-
PARI
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(3*(1-exp(x)))/3))) -
PARI
a(n) = sum(k=1, n, (3*k)^(k-1)*stirling(n, k, 2));
Formula
E.g.f.: -LambertW(3 * (1 - exp(x)))/3.
a(n) = Sum_{k=1..n} (3 * k)^(k-1) * Stirling2(n,k).
a(n) ~ sqrt(1 + 3*exp(1)) * n^(n-1) / (3 * exp(n) * log(1 + exp(-1)/3)^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( log(1 + x * exp(-3*x)) ). - Seiichi Manyama, Sep 09 2024