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A134161
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a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4.
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5
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373, 10363, 61723, 210901, 539041, 1151983, 2180263, 3779113, 6128461, 9432931, 13921843, 19849213, 27493753, 37158871, 49172671, 63887953, 81682213, 102957643, 128141131, 157684261, 192063313, 231779263, 277357783, 329349241
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = (3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 5}]
G.f.: -(373+8498*x+13638*x^2+2186*x^3+x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) with a(0)=373, a(1)=10363, a(2)=61723, a(3)=210901, and a(4)=539041. - Harvey P. Dale, Nov 25 2012
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MATHEMATICA
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1) Table[(3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}] (*Artur Jasinski*)
LinearRecurrence[{5, -10, 10, -5, 1}, {373, 10363, 61723, 210901, 539041}, 100] (* Harvey P. Dale, Nov 25 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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