OFFSET
0,3
COMMENTS
a(n) is the sum of all products of two distinct elements from the set {1^5, ..., n^5}.
LINKS
Roudy El Haddad, Multiple Sums and Partition Identities, arXiv:2102.00821 [math.CO], 2021.
Roudy El Haddad, A generalization of multiple zeta value. Part 2: Multiple sums. Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 200-233, DOI: 10.7546/nntdm.2022.28.2.200-233.
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
a(n) = Sum_{j=2..n} Sum_{i=1..j-1} j^5*i^5.
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.
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
PROG
(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};
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roudy El Haddad, Feb 19 2022
STATUS
approved