A332236 E.g.f.: -log(2 - 1 / (1 + LambertW(-x))).

1, 5, 41, 466, 6769, 119736, 2497585, 60037328, 1634619969, 49733223040, 1672657257721, 61636181886720, 2470033974057649, 106970912288285696, 4979259164362745025, 247940951411958163456, 13152705012933836446465, 740578125097986605678592, 44115815578591964641401289

Offset: 1

Author

Ilya Gutkovskiy, Feb 07 2020

Keywords

• nonn

Crossrefs

Cf. A000312, A001865, A133297, A202477, A210661, A308863, A323673, A332237.

Programs

Mathematica

nmax = 19; CoefficientList[Series[-Log[2 - 1/(1 + LambertW[-x])], {x, 0, nmax}], x] Range[0, nmax]! // Rest
a[n_] := a[n] = n^n + (1/n) Sum[Binomial[n, k] (n - k)^(n - k) k a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]

Formula

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

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

a(n) ~ (n-1)! * 2^n * exp(n/2). - Vaclav Kotesovec, Feb 16 2020