A303916 Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^3.
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
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Crossrefs
Column 3 of A322549.
Programs
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GAP
List([0..35],n->(n-1)*n*(n+1)*(n+2)*(2*n+1)/10); # Muniru A Asiru, Dec 16 2018
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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 *)
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PARI
{a(n) = polcoeff((sum(k=0, n, k*(x^k+x^(-k))))^3, 0, x)}
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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.