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A351146
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a(n) = Sum_{k=1..n} binomial(2*n,n+k)*A000005(k).
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11
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1, 6, 29, 131, 572, 2448, 10341, 43288, 180003, 744712, 3068793, 12605411, 51642528, 211110240, 861409918, 3509341245, 14277424978, 58017460260, 235512889296, 955146370152, 3870511127394, 15672817355658, 63421721139479, 256488917828150, 1036722699748068, 4188329011110360
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OFFSET
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1,2
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REFERENCES
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D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 3, Sorting and Searching. Chapter 5.2.2 Sorting by Exchanging, pages 138 (exercise 52), 637 (answer to exercise). Addison-Wesley, Reading, MA, 1998.
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LINKS
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FORMULA
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a(n) ~ 4^(n-1) * (log(n/4) + 3*gamma + 1/sqrt(Pi*n)) [Knuth, 1998]. - Vaclav Kotesovec, Aug 04 2022
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MATHEMATICA
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Table[Sum[Binomial[2*n, n + k] * DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 04 2022 *)
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PROG
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(PARI) a(n) = sum(k=1, n, binomial(2*n, n+k)*numdiv(k)); \\ Michel Marcus, Feb 02 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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