A300299 Denominators of r(n) := Sum_{k=0..n-1} 1/Product_{j=0..4} (k + j + 1), for n >= 0, with r(0) = 0.

1, 120, 720, 1680, 2240, 12096, 20160, 31680, 23760, 11440, 12012, 32760, 174720, 76160, 293760, 372096, 116280, 17955, 117040, 425040, 1020096, 1214400, 478400, 1684800, 982800, 1140048, 657720, 125860, 3452160, 3928320

Offset: 0

Author

Wolfdieter Lang, Apr 05 2018

Keywords

• nonn
• frac
• easy

Comments

For the numerators see A300298, also for a comment and the Jolley reference. The g.f. of {r(n)}_{n>=0} and examples are given there too.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A300298.

Programs

GAP

List(List([0..40],n->Sum([0..n-1],k->1/(Product([0..4],j->k+j+1)))),DenominatorRat); # Muniru A Asiru, Apr 05 2018

Magma

[Denominator(n*(50+35*n+10*n^2+n^3)/(96*(1+n)*(2+n)*(n+3)*(4+n))): n in [0..50]]; // Vincenzo Librandi, Apr 06 2018

Mathematica

Table[Denominator[n (50 + 35 n + 10 n^2 + n^3) / (96 (1 + n)(2 + n) (n + 3) (4 + n))], {n, 0, 50}] (* Vincenzo Librandi, Apr 06 2018 *)

PARI

a(n) = denominator(sum(k=0, n-1, prod(j=0, 4, (k+j+1))^(-1))); \\ Altug Alkan, Apr 05 2018

Formula

a(n) = denominator(r(n)), with the result of the sum given in the name r(n) = n*(50 + 35*n + 10*n^2 + n^3)/(96*(1 + n)*(2 + n)*(n + 3)*(4 + n)), n >= 0.