A132341 Main diagonal of A132339.

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

Offset

0,2

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A132339.

Sequence in context: A328812 A126451 A260122 * A069994 A063573 A368573

Adjacent sequences: A132338 A132339 A132340 * A132342 A132343 A132344

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 08 2007

Extensions

More terms from Max Alekseyev, Sep 12 2009

Status

approved