A305276 Expansion of e.g.f. 1/(1 + LambertW(-x/(1 - x))).
1, 1, 6, 57, 748, 12565, 257526, 6232765, 173980920, 5502613833, 194477548330, 7596028355641, 324920533473108, 15106155118606045, 758463525318426942, 40901033617318501845, 2357682497456804486896, 144670077586483815863569, 9414952083720893890165842, 647715776085173413399687633
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..369
- N. J. A. Sloane, Transforms
Programs
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Maple
S:= series(1/(1+LambertW(-x/(1-x))),x,51): seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Aug 19 2018
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Mathematica
nmax = 19; CoefficientList[Series[1/(1 + LambertW[-x/(1 - x)]), {x, 0, nmax}], x] Range[0, nmax]! Join[{1}, Table[Sum[Binomial[n - 1, k - 1] k^k n!/k!, {k, n}], {n, 19}]]
Formula
a(n) = Sum_{k=0..n} binomial(n-1,k-1)*k^k*n!/k!.
a(n) ~ n^n * (1 + exp(1))^(n - 1/2) / exp(n - 1/2). - Vaclav Kotesovec, Aug 18 2018
Comments