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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
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.
Sequence in context: A173413 A008549 A345031 * A026675 A026873 A081179
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.)