OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
E.g.f.: exp( -LambertW(x * log(1-x)) ).
E.g.f.: LambertW(x * log(1-x)) / (x * log(1-x)).
a(n) ~ sqrt(1 + exp(1)*r^2/(1-r)) * n^(n-1) / (exp(n-1) * r^n), where r = 0.5123112855238643734867005914814802444318611742265... is the positive root of the equation r*log(1-r) = -exp(-1). - Vaclav Kotesovec, Jul 21 2022
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!. - Seiichi Manyama, Aug 28 2022
MATHEMATICA
nmax = 20; CoefficientList[Series[LambertW[x * Log[1-x]] / (x * Log[1-x]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 21 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(x*log(1-x)))))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!); \\ Seiichi Manyama, Aug 28 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 18 2022
STATUS
approved