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A264892
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a(n) = n*(3*n - 2)*(9*n^2 - 6*n - 2).
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2
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0, 1, 176, 1281, 4720, 12545, 27456, 52801, 92576, 151425, 234640, 348161, 498576, 693121, 939680, 1246785, 1623616, 2080001, 2626416, 3273985, 4034480, 4920321, 5944576, 7120961, 8463840, 9988225, 11709776, 13644801, 15810256, 18223745, 20903520
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OFFSET
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0,3
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COMMENTS
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Doubly octagonal numbers.
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LINKS
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FORMULA
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G.f.: x*(1 + 171*x + 411*x^2 + 65*x^3)/(1 - x)^5.
Sum_{n>0} 1/a(n) = (sqrt(3)*gamma + sqrt(3)*polygamma(0, 1/3) - polygamma(0, (1/3)*(2 - sqrt(3))) + polygamma(0, (1/3)*(2 + sqrt(3))))/(4*sqrt(3)) = 1.006842786293...,where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.
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MATHEMATICA
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Table[n (3 n - 2) (9 n^2 - 6 n - 2), {n, 0, 30}]
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PROG
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(PARI) concat(0, Vec(x*(1+171*x+411*x^2+65*x^3)/(1-x)^5 + O(x^100))) \\ Altug Alkan, Nov 27 2015
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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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