A256194 a(n) = denominator of n!*n^n*Product_{k=0..n} 1/(n*k + n - 1).

15, 440, 21945, 277704, 178986115, 215289360, 107174712645, 2019114114160, 5162399729063577, 310327149656160, 264020420256172514935, 555320997799108800, 183986274976015448239875, 7616449380979972355121376, 132186242095677958872242925, 3493664585524176681103200

Offset: 2

Author

Michel Marcus, Mar 19 2015

Keywords

• nonn
• frac

Comments

n!*n^n*Product_{k=0..n} 1/(n*k + n - 1) = Sum_{k=0..n} (-1)^k*binomial(n,k)/(n*k + n - 1) (see arXiv link).

Links

• Brett Pansano, An Interesting Identity, arXiv:1503.04678 [math.GM], 2015.

Crossrefs

Cf. A145921 (numerators).

Programs

Mathematica

Table[Denominator[n! n^n Product[1/(n k + n - 1), {k, 0, n}]], {n, 2, 17}] (* Jean-François Alcover, Sep 26 2018 *)

PARI

a(n) = denominator(sum(k=0, n, (-1)^k*binomial(n,k)/(n*k+n-1)));