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%I #19 Nov 15 2022 14:22:10
%S 0,39,196,664,1809,4250,8954,17346,31434,53949,88500,139744,213571,
%T 317304,459914,652250,907284,1240371,1669524,2215704,2903125,3759574,
%U 4816746,6110594,7681694,9575625,11843364,14541696,17733639,21488884,25884250,31004154,36941096
%N a(n) = (1/48)*n*(n+5)^2*(1*n^3 + 7*n^2 + 16*n + 28).
%H Colin Barker, <a href="/A290071/b290071.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F From _Colin Barker_, Jul 20 2017: (Start)
%F G.f.: x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6.
%F (End)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,39,196,664,1809,4250,8954},40] (* _Harvey P. Dale_, Nov 15 2022 *)
%o (PARI) concat(0, Vec(x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7 + O(x^50))) \\ _Colin Barker_, Jul 20 2017
%o (PARI) vector(50,n,n*(n+5)^2*(n^3+7*n^2+16*n+28)/48) \\ _Derek Orr_, Jul 24 2017
%Y This is the negation of column 4 in triangle A290053.
%K nonn,easy
%O 0,2
%A _Gregory Gerard Wojnar_, Jul 19 2017
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