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

Author

Hugo Pfoertner, Feb 02 2022

Keywords

• nonn

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

Crossrefs

Diagonal of A351145.

Cf. A000005, A356338, A356339, A356340.

Programs

Mathematica

Table[Sum[Binomial[2*n, n + k] * DivisorSigma[0, k], {k, 1, n}], {n,1,20}] (* Vaclav Kotesovec, Aug 04 2022 *)

PARI

a(n) = sum(k=1, n, binomial(2*n, n+k)*numdiv(k)); \\ Michel Marcus, Feb 02 2022

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