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 A351146 a(n) = Sum_{k=1..n} binomial(2*n,n+k)*A000005(k). 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..1650 FORMULA a(n) = A351145(n,n). a(n) ~ 4^(n-1) * (log(n/4) + 3*gamma + 1/sqrt(Pi*n)) [Knuth, 1998]. - Vaclav Kotesovec, Aug 04 2022 MATHEMATICA Table[Sum[Binomial[2*n, n + k] * DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 04 2022 *) PROG (PARI) a(n) = sum(k=1, n, binomial(2*n, n+k)*numdiv(k)); \\ Michel Marcus, Feb 02 2022 CROSSREFS Diagonal of A351145. Cf. A000005, A356338, A356339, A356340. Sequence in context: A173413 A008549 A345031 * A026675 A026873 A081179 Adjacent sequences: A351143 A351144 A351145 * A351147 A351148 A351149 KEYWORD nonn AUTHOR Hugo Pfoertner, Feb 02 2022 STATUS approved

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Last modified July 12 18:45 EDT 2024. Contains 374251 sequences. (Running on oeis4.)