A130863 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).

0, 30, 100, 231, 448, 780, 1260, 1925, 2816, 3978, 5460, 7315, 9600, 12376, 15708, 19665, 24320, 29750, 36036, 43263, 51520, 60900, 71500, 83421, 96768, 111650, 128180, 146475, 166656, 188848

Offset

1,2

Comments

Double sum ratio is: A055998

Links

Table of n, a(n) for n=1..30.

Formula

a(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}]=(1/6)*(-1 + n)(2 + n)(3 + n)(7 + n)

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

Mathematica

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}]

Crossrefs

Cf. A055998.

Sequence in context: A002758 A346855 A187401 * A070114 A070132 A280911

Adjacent sequences: A130860 A130861 A130862 * A130864 A130865 A130866

Keyword

nonn

Author

Roger L. Bagula, Jul 22 2007

Status

approved