login
A357333
E.g.f. satisfies A(x) = -log(1 - x) * exp(2 * A(x)).
3
0, 1, 5, 50, 778, 16604, 451668, 14947568, 582982160, 26187136128, 1331445995520, 75589772147328, 4739901861071232, 325353447339098112, 24264683011603485696, 1953776475810372817920, 168924939633683095452672, 15609228287753846217412608
OFFSET
0,3
FORMULA
E.g.f.: -LambertW(2 * log(1 - x))/2.
a(n) = Sum_{k=1..n} (2 * k)^(k-1) * |Stirling1(n,k)|.
a(n) ~ n^(n-1) / (sqrt(2) * (exp(exp(-1)/2)-1)^(n - 1/2) * exp(n - n*exp(-1)/2 - 1/2)). - Vaclav Kotesovec, Oct 04 2022
E.g.f.: Series_Reversion( 1 - exp(-x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024
MATHEMATICA
nmax = 17; A[_] = 0;
Do[A[x_] = -Log[1 - x]*Exp[2*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 05 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(2*log(1-x))/2)))
(PARI) a(n) = sum(k=1, n, (2*k)^(k-1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved