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%I #23 Aug 08 2019 19:57:54
%S 0,0,560,14240,146680,922680,4226040,15492680,48144680,131678360,
%T 325322360,739761880,1570082800,3143824320,5988841040,10926565040,
%U 19197225520,32624627920,53829216160,86499340720,135731931720,208455129960,313946860040,464464838200
%N Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^5.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = (n-1) * n * (n+1) * (2*n+1) * (967*n^5+3868*n^4+6005*n^3+5444*n^2+2844*n+1008) / 9072.
%t a[n_] := Coefficient[Expand[Sum[k * (x^k + x^(-k)), {k, 0, n}]^5], x, 0]; Array[a, 30, 0] (* _Amiram Eldar_, Dec 16 2018 *)
%o (PARI) {a(n) = polcoeff((sum(k=0, n, k*(x^k+x^(-k))))^5, 0, x)}
%o (PARI) {a(n) = (n-1)*n*(n+1)*(2*n+1)*(967*n^5+3868*n^4+6005*n^3+5444*n^2+2844*n+1008)/9072}
%o (GAP) List([0..25],n->(n-1)*n*(n+1)*(2*n+1)*(967*n^5+3868*n^4+6005*n^3+5444*n^2+2844*n+1008)/9072); # _Muniru A Asiru_, Dec 16 2018
%Y Column 5 of A322549.
%Y Cf. A083669.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Dec 16 2018
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