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A343547
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a(n) = n * Sum_{d|n} binomial(d+n-2,n-1)/d.
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8
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1, 4, 9, 32, 75, 318, 931, 3712, 13014, 50110, 184767, 715656, 2704169, 10454976, 40126395, 155462016, 601080407, 2335849578, 9075135319, 35359120940, 137847221148, 538346579034, 2104098963743, 8234009441952, 32247603785500, 126414311404108, 495918587420145
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = [x^n] Sum_{k>=1} k * x^k/(1 - x^k)^n.
a(n) = [x^n] Sum_{k>=1} binomial(k+n-2,n-1) * x^k/(1 - x^k)^2.
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MATHEMATICA
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a[n_] := n * DivisorSum[n, Binomial[# + n - 2, n-1]/# &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)
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PROG
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(PARI) a(n) = n*sumdiv(n, d, binomial(d+n-2, n-1)/d);
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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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