A130863 - OEIS

%I #9 Jan 27 2025 06:46:47

%S 0,30,100,231,448,780,1260,1925,2816,3978,5460,7315,9600,12376,15708,

%T 19665,24320,29750,36036,43263,51520,60900,71500,83421,96768,111650,

%U 128180,146475,166656,188848

%N Ratio of quadruple Sum of k^2-1 to quadruple sum of k made into an integer sequence: (1/6)*(-1 + n)*(2 + n)*(3 + n)*(7 + n).

%C Double sum ratio is: A055998.

%F a(n) = (1/2)*(n + 2)*(n + 3)*(n + 4)*(Sum_{l=1..n} Sum_{j=1..l} Sum_{m=1..j} Sum_{k=1..m} (k^2 - 1))/(Sum_{l=1..n} Sum_{j=1..l} Sum_{m=1..j} Sum_{k=1..m} k).

%F a(n) = (1/6)*(-1 + n)*(2 + n)*(3 + n)*(7 + n).

%F G.f.: x^2*(-30+50*x-31*x^2+7*x^3)/(-1+x)^5. - _R. J. Mathar_, Nov 14 2007

%t h[n_] = (1/2)*(n + 2)*(n + 3)*(n + 4)*Sum[Sum[Sum[Sum[k^2 - 1, {k, 1, m}], {m, 1, j}], {j, 1, l}], {l, 1, n}]/Sum[Sum[Sum[Sum[k, {k, 1, m}], {m, 1, j}], {j, 1, l}], {l, 1, n}]; Table[h[n], {n, 1, 30}]

%Y Cf. A055998.

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, Jul 22 2007