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Search: id:A130863
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| A130863 |
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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). |
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+0
1
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| 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
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OFFSET
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1,2
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COMMENT
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Double sum ratio is: A055998
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FORMULA
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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 (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A055998.
Sequence in context: A096382 A008525 A002758 this_sequence A070114 A070132 A043218
Adjacent sequences: A130860 A130861 A130862 this_sequence A130864 A130865 A130866
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KEYWORD
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nonn
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AUTHOR
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Roger L Bagula (rlbagulatftn(AT)yahoo.com), Jul 22 2007
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