A336250 a(n) = (n!)^n * Sum_{k=1..n} (-1)^(k+1) / k^n.

0, 1, 3, 197, 313840, 24191662624, 137300308036448256, 81994640912971156525105152, 6958651785463110878359050928999366656, 108902755985567407887534498777329973193771818418176, 395560567918154447056086270973712023435510589158871531520000000000

Offset: 0

Author

Ilya Gutkovskiy, Jul 14 2020

Keywords

• nonn

Crossrefs

Cf. A024167, A036740, A060943, A142999.

Programs

Mathematica

Table[(n!)^n Sum[(-1)^(k + 1)/k^n, {k, 1, n}], {n, 0, 10}]
Table[(n!)^n SeriesCoefficient[-PolyLog[n, -x]/(1 - x), {x, 0, n}], {n, 0, 10}]

PARI

a(n) = (n!)^n * sum(k=1, n, (-1)^(k+1) / k^n); \\ Michel Marcus, Jul 14 2020

Formula

a(n) = (n!)^n * [x^n] -polylog(n,-x) / (1 - x).