VOOZH about

URL: https://oeis.org/A351805

⇱ A351805 - OEIS

login
A351805
a(n) = Sum_{1 <= i < j <= n} j^5*i^5.
0
0, 0, 32, 8051, 290675, 4353175, 38761975, 243824182, 1194358326, 4842169350, 16924669350, 52488756425, 147511725257, 381689190701, 920589376525, 2089893985900, 4500779925100, 9254143113132, 18262909865676, 34746798604575, 63973358604575, 114343801467875
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
Cf. A000217 (for power 0), A000914 (for power 1), A000596 (for squares), A347107 (for cubes), (for fourth powers).
Cf. A000584 (fifth powers), A000539 (sum of fifth powers).
Sequence in context: A069052 A334604 A342455 * A221614 A086752 A248001
KEYWORD
nonn,easy
AUTHOR
Roudy El Haddad, Feb 19 2022
STATUS
approved