A132341 Main diagonal of A132339.

1, 2, 10, 168, 4290, 136136, 4938024, 196125600, 8318177010, 370784099400, 17184867259560, 821870841735840, 40334204896057800, 2022686389717666848, 103312949950998743200, 5360873347802169267840, 282015983963437605168210

Offset: 0

Author

N. J. A. Sloane, Nov 08 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, 6 (1965), see equation (67) circa p. 82.

Crossrefs

Cf. A132339.

Programs

Mathematica

a[n_]:= If[n==0, 1, Binomial[2*n, n]*Binomial[4*n-2, 2*n-1]/(2*Binomial[2*n,2])];
Table[a[n], {n, 0, 20}] (* G. C. Greubel, Dec 14 2021 *)

PARI

a(n) = if (n, 2*(4*n-3)!/(n!^2*(2*n-1)!), 1); \\ Michel Marcus, Mar 27 2016

Sage

b=binomial
def a(n): return 1 if (n==0) else b(2*n, n)*b(4*n-2, 2*n-1)/(2*b(2*n,2))
[a(n) for n in (0..20)] # G. C. Greubel, Dec 14 2021

Formula

a(n) = T(n, n), where T(n,k) if the array of A132339.

a(n) = A(2*n, n), where A(n, k) is the antidiagonal triangle of A132339.

a(n) ~ 2^(6*n - 9/2) / (Pi*n^3). - Vaclav Kotesovec, Mar 27 2016

a(n) = binomial(2*n, n)*binomial(4*n-2, 2*n-1)/((2*n)*(2*n-1)), with a(0) = 1. - G. C. Greubel, Dec 14 2021

Extensions

More terms from Max Alekseyev, Sep 12 2009