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A300847
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a(n) = 12*binomial(n, 5).
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0
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0, 0, 0, 0, 0, 12, 72, 252, 672, 1512, 3024, 5544, 9504, 15444, 24024, 36036, 52416, 74256, 102816, 139536, 186048, 244188, 316008, 403788, 510048, 637560, 789360, 968760, 1179360, 1425060, 1710072, 2038932, 2416512, 2848032, 3339072, 3895584, 4523904, 5230764
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OFFSET
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0,6
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COMMENTS
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Also the number of 5-cycles in the complete graph K_n for n >= 1.
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LINKS
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FORMULA
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G.f.: 12*x^5/(x - 1)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) + 6*a(n-4) - a(n-5).
a(n) = (n - 4)*(n - 3)*(n - 2)*(n - 1)*n/10.
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MATHEMATICA
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Table[12 Binomial[n, 5], {n, 0, 20}]
12 Binomial[Range[0, 20], 5]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 0, 12, 72}, {0, 20}]
CoefficientList[Series[12 x^5/(x - 1)^6, {x, 0, 20}], x]
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PROG
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(PARI) a(n) = 12*binomial(n, 5); \\ Altug Alkan, Mar 13 2018
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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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