A351146 a(n) = Sum_{k=1..n} binomial(2*n,n+k)*A000005(k).

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

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