A331582 a(n) = n! * [x^n] exp(n - exp(x) * (exp(n*x) - 1) / (exp(x) - 1)).

1, -1, 4, 0, -1654, 102750, -4079389, -178722208, 83191059372, -14561829897345, 1115121827539325, 403631463559529040, -251989999508801085674, 76158421344845152140737, -3994730250899559184766830, -13162858116922635098226480000, 10823217968258750568539067678392

Offset: 0

Author

Ilya Gutkovskiy, Jan 21 2020

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A103438, A319508, A319509, A320288.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n - Exp[x] (Exp[n x] - 1)/(Exp[x] - 1)], {x, 0, n}], {n, 0, 16}]
b[n_, k_] := b[n, k] = If[n == 0, 1, -Sum[Binomial[n - 1, j - 1] Sum[i^j, {i, 1, k}] b[n - j, k], {j, 1, n}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 16}]

Formula

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