A319509 a(n) = n! * [x^n] 1/(1 - n + exp(x)*(exp(n*x) - 1)/(exp(x) - 1)).

1, -1, 13, -828, 145046, -53306325, 35351663831, -38335940184976, 63385171527442332, -151639317344211911505, 503956292395339783686325, -2252032996384696958326480356, 13175456854397460097168816336930, -98695402553214372025148083384255381

Offset: 0

Author

Ilya Gutkovskiy, Sep 21 2018

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..167

Crossrefs

Cf. A319508.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 - n + Exp[x] (Exp[n x] - 1)/(Exp[x] - 1)), {x, 0, n}], {n, 0, 13}]

PARI

default(seriesprecision, 101); {a(n) = n!*polcoeff((1/(1-n+exp(x)*(exp(n*x)-1)/(exp(x)-1)) + O(x^(n+1))), n)};
for(n=0, 25, print1(a(n), ", ")) \\ G. C. Greubel, Oct 09 2018

Formula

a(n) = n! * [x^n] 1/(1 - n + exp(x) + exp(2*x) + exp(3*x) + ... + exp(n*x)).