A332237 - OEIS

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A332237

E.g.f.: -log(1 + LambertW(-x) * (2 + LambertW(-x)) / 2).

1, 2, 8, 49, 409, 4356, 56734, 877094, 15742521, 322454800, 7434673036, 190792267128, 5398552673617, 167087263076384, 5617979017621650, 203987454978218416, 7957053981454827601, 331920300203780633856, 14746208516909980554736, 695208730205550274544000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

FORMULA

E.g.f.: -log(1 - Sum_{k>=1} k^(k-2) * x^k / k!).

a(n) = n^(n-2) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * (n-k)^(n-k-2) * k * a(k).

a(n) ~ 2 * n^(n-2). - Vaclav Kotesovec, Feb 16 2020

MATHEMATICA

nmax = 20; CoefficientList[Series[-Log[1 + LambertW[-x] (2 + LambertW[-x])/2], {x, 0, nmax}], x] Range[0, nmax]! // Rest

a[n_] := a[n] = n^(n - 2) + (1/n) Sum[Binomial[n, k] (n - k)^(n - k - 2) k a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]