A352979 a(n) = Sum_{k=1..n} Sum_{j=1..k} Sum_{i=1..j} (k*j*i)^3.
0, 1, 585, 28800, 505280, 4951530, 33209946, 170320080, 714724560, 2566030995, 8130545995, 23253835176, 61054704360, 149085989780, 342048076020, 743408003520, 1540821690816, 3062326169925, 5862986735085, 10855192630480, 19500255870480
Offset: 0
References
- El Haddad, R. (2022). A generalization of multiple zeta value. Part 1: Recurrent sums. Notes on Number Theory and Discrete Mathematics, 28(2), 167-199, DOI: 10.7546/nntdm.2022.28.2.167-199.
Links
- Roudy El Haddad, Recurrent Sums and Partition Identities, arXiv:2101.09089 [math.NT], 2021.
- Roudy El Haddad, A generalization of multiple zeta value. Part 1: Recurrent sums. Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 167-199, DOI: 10.7546/nntdm.2022.28.2.167-199.
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1). [Typo corrected by _Georg Fischer_, Sep 30 2022]
Crossrefs
Programs
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PARI
{a(n) = n^2 * (n + 1)^2 * (n + 2) * (n + 3) * (35*n^6 + 205*n^5 + 263*n^4 - 221*n^3 - 214*n^2 + 324*n - 112)/13440}; -
Python
def A352979(n): return n**2*(n*(n*(n*(n*(n*(n*(n*(n*(n*(35*n + 450) + 2293) + 5700) + 6405) + 770) - 3661) - 240) + 2320) + 40) - 672)//13440 # Chai Wah Wu, May 14 2022
Formula
a(n) = n^2 * (n + 1)^2 * (n + 2) * (n + 3) * (35*n^6 + 205*n^5 + 263*n^4 - 221*n^3 - 214*n^2 + 324*n - 112)/13440.
a(n) = binomial(n+3,4)*binomial(n+1,2)*(35*n^6 + 205*n^5 + 263*n^4 - 221*n^3 - 214*n^2 + 324*n - 112)/280.
Comments