cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A303916 Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^3.

Original entry on oeis.org

0, 0, 12, 84, 324, 924, 2184, 4536, 8568, 15048, 24948, 39468, 60060, 88452, 126672, 177072, 242352, 325584, 430236, 560196, 719796, 913836, 1147608, 1426920, 1758120, 2148120, 2604420, 3135132, 3749004, 4455444, 5264544, 6187104, 7234656, 8419488, 9754668
Offset: 0

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Author

Seiichi Manyama, Dec 16 2018

Keywords

Crossrefs

Column 3 of A322549.

Programs

  • GAP
    List([0..35],n->(n-1)*n*(n+1)*(n+2)*(2*n+1)/10); # Muniru A Asiru, Dec 16 2018
  • Mathematica
    a[n_] := Coefficient[Expand[Sum[k * (x^k + x^(-k)), {k, 0, n}]^3], x, 0]; Array[a, 30, 0] (* Amiram Eldar, Dec 16 2018 *)
    Table[((n-1)n(n+1)(n+2)(2n+1))/10,{n,0,50}] (* Harvey P. Dale, Jul 01 2019 *)
  • PARI
    {a(n) = polcoeff((sum(k=0, n, k*(x^k+x^(-k))))^3, 0, x)}
    
  • PARI
    {a(n) = (n-1)*n*(n+1)*(n+2)*(2*n+1)/10}
    

Formula

a(n) = (n-1) * n * (n+1) * (n+2) * (2*n+1) / 10.