cp's OEIS Frontend

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.

%I A300299 #17 Sep 08 2022 08:46:20
%S A300299 1,120,720,1680,2240,12096,20160,31680,23760,11440,12012,32760,174720,
%T A300299 76160,293760,372096,116280,17955,117040,425040,1020096,1214400,
%U A300299 478400,1684800,982800,1140048,657720,125860,3452160,3928320
%N 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.
%C A300299 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.
%H A300299 Muniru A Asiru, <a href="/A300299/b300299.txt">Table of n, a(n) for n = 0..5000</a>
%F A300299 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.
%t A300299 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 *)
%o A300299 (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
%o A300299 (PARI) a(n) = denominator(sum(k=0, n-1, prod(j=0, 4, (k+j+1))^(-1))); \\ _Altug Alkan_, Apr 05 2018
%o A300299 (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
%Y A300299 Cf. A300298.
%K A300299 nonn,frac,easy
%O A300299 0,2
%A A300299 _Wolfdieter Lang_, Apr 05 2018