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A356345
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a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma_2(k).
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0
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2, 32, 232, 1702, 8254, 54454, 226054, 1320004, 5744424, 29762704, 115825408, 683698168, 2451800168, 12480950168, 52811505368, 257779918358, 934525722158, 5063712283658, 17858697779258, 93122902514978, 362251839734978, 1645752207604178, 6009470493232178, 33419933623867178
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OFFSET
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1,1
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COMMENTS
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The average value of a(n) is zeta(3) * n^(3/2) * 4^(n+1) / (3*sqrt(Pi)).
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LINKS
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MATHEMATICA
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Table[Sum[Binomial[2*k, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
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PROG
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(PARI) a(n) = sum(k=1, n, binomial(2*k, k) * sigma(k, 2)); \\ Michel Marcus, Aug 05 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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