cp's OEIS Frontend

A351805 a(n) = Sum_{1 <= i < j <= n} j^5*i^5.

%I A351805 #14 Jun 05 2022 01:07:23
%S A351805 0,0,32,8051,290675,4353175,38761975,243824182,1194358326,4842169350,
%T A351805 16924669350,52488756425,147511725257,381689190701,920589376525,
%U A351805 2089893985900,4500779925100,9254143113132,18262909865676,34746798604575,63973358604575,114343801467875
%N A351805 a(n) = Sum_{1 <= i < j <= n} j^5*i^5.
%C A351805 a(n) is the sum of all products of two distinct elements from the set {1^5, ..., n^5}.
%H A351805 Roudy El Haddad, <a href="https://arxiv.org/abs/2102.00821">Multiple Sums and Partition Identities</a>, arXiv:2102.00821 [math.CO], 2021.
%H A351805 Roudy El Haddad, <a href="https://doi.org/10.7546/nntdm.2022.28.2.200-233">A generalization of multiple zeta value. Part 2: Multiple sums</a>. Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 200-233, DOI: 10.7546/nntdm.2022.28.2.200-233.
%H A351805 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A351805 a(n) = Sum_{j=2..n} Sum_{i=1..j-1} j^5*i^5.
%F A351805 a(n) = n*(n - 1)*(n + 1)*(44*n^9 + 120*n^8 - 132*n^7 - 540*n^6 + 99*n^5 + 912*n^4 - 11*n^3 - 672*n^2 + 120)/3168.
%F A351805 G.f.: -x^2*(x^9 +1044*x^8 +54462*x^7 +595860*x^6 +2048388*x^5 +2563644*x^4 +1193226*x^3 +188508*x^2 +7635*x +32)/(x-1)^13. - _Alois P. Heinz_, Feb 19 2022
%o A351805 (PARI) {a(n) = n*(n-1)*(n+1)*(44*n^9+120*n^8-132*n^7-540*n^6+99*n^5+912*n^4-11*n^3-672*n^2+120)/3168};
%Y A351805 Cf. A000217 (for power 0), A000914 (for power 1), A000596 (for squares), A347107 (for cubes), (for fourth powers).
%Y A351805 Cf. A000584 (fifth powers), A000539 (sum of fifth powers).
%K A351805 nonn,easy
%O A351805 0,3
%A A351805 _Roudy El Haddad_, Feb 19 2022