A292633 a(n) = n! * [x^n] -exp(n*x)*LambertW(-x).

0, 1, 6, 54, 656, 10100, 189252, 4195870, 107803712, 3158565192, 104179336100, 3827097857594, 155176637687568, 6890781261435916, 332846314505306084, 17384125179840159150, 976545328548757184768, 58723524484105985029136, 3764267361608204263229892, 256245748998712921762125922

Offset: 0

Author

Ilya Gutkovskiy, Sep 20 2017

Keywords

• nonn

Comments

The n-th term of the n-th binomial transform of A000169.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..365
• N. J. A. Sloane, Transforms

Crossrefs

Main diagonal of A294411.

Cf. A000169, A290840.

Programs

Mathematica

Table[n!*SeriesCoefficient[-E^(n*x)*LambertW[-x],{x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Sep 20 2017 *)

Formula

a(n) ~ exp(n*exp(-1)) * n^(n-1) / (1-exp(-1))^(3/2). - Vaclav Kotesovec, Sep 20 2017