login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132341 Main diagonal of A132339. 2
1, 2, 10, 168, 4290, 136136, 4938024, 196125600, 8318177010, 370784099400, 17184867259560, 821870841735840, 40334204896057800, 2022686389717666848, 103312949950998743200, 5360873347802169267840, 282015983963437605168210 (list; graph; refs; listen; history; text; internal format)
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 A356887

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 09:41 EST 2022. Contains 358610 sequences. (Running on oeis4.)