A060856 Multi-dimensional Catalan numbers: diagonal T(n,n+2) of A060854.

1, 14, 6006, 140229804, 278607172289160, 67867669180627125604080, 2760171874087743799855959353857200, 24486819823897171791550434989846505231774984000, 59986874261544072491135645330451363110127974096720977464312000

Offset: 1

Author

R. H. Hardin, May 03 2001

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..29

Crossrefs

Cf. A060854, A074962.

Cf. A039622.

Programs

Mathematica

Table[Product[j!/(n+j)!,{j,0,n+1}]*(n*(n+2))!,{n,1,10}] (* Vaclav Kotesovec, Mar 09 2015 *)

Formula

a(n) = 0!*1!*...*(k-1)! *(k*n)! / ( n!*(n+1)!*...*(n+k-1)! ) for k=n+2.

a(n) ~ sqrt(Pi) * exp(n^2/2 + 2*n + 25/12) * n^(n^2 + 2*n + 11/12) / (A * 2^(2*n^2 + 4*n + 17/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 09 2015

a(n) = A039622(n+1) / (n+1). - Tom Copeland, May 30 2022