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%I #13 Sep 08 2022 08:45:02
%S 1,10,44,133,319,656,1210,2059,3293,5014,7336,10385,14299,19228,25334,
%T 32791,41785,52514,65188,80029,97271,117160,139954,165923,195349,
%U 228526,265760,307369,353683,405044,461806,524335,593009,668218,750364,839861,937135
%N (1/2)*(n^2+n+2)*(n^2+3*n+1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = sum(i, i = n..(n+1)^2).
%F G.f.: (1+5*x+4*x^2+3*x^3-x^4)/(1-x)^5; a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Sep 14 2014
%p A058310:=n->(n^2+n+2)*(n^2+3*n+1)/2: seq(A058310(n), n=0..40); # _Wesley Ivan Hurt_, Sep 14 2014
%t Table[(n^2 + n + 2) (n^2 + 3 n + 1)/2, {n, 0, 40}] (* _Wesley Ivan Hurt_, Sep 14 2014 *)
%t CoefficientList[Series[(1 + 5 x + 4 x^2 + 3 x^3 - x^4)/(1 - x)^5, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 14 2014 *)
%o (Magma) [(n^2+n+2)*(n^2+3*n+1)/2 : n in [0..40]]; // _Wesley Ivan Hurt_, Sep 14 2014
%o (PARI) Vec((1+5*x+4*x^2+3*x^3-x^4)/(1-x)^5 + O(x^50)) \\ _Michel Marcus_, Sep 15 2014
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 09 2000
%E More terms from _Wesley Ivan Hurt_, Sep 14 2014
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