A060855 Multi-dimensional Catalan numbers: diagonal T(n,n+1) of A060854.

1, 5, 462, 1662804, 396499770810, 9490348077234178440, 32103104214166146088869942000, 20535535214275361308250745082811167425600, 3201252689605333194364294895470993505956118059617444000

Offset: 1

Author

R. H. Hardin, May 03 2001

Keywords

• nonn
• easy

Comments

Number of standard tableaux of shape ((n+1)^n). - Emeric Deutsch, May 13 2004

Links

• G. C. Greubel, Table of n, a(n) for n = 1..29
• Zachary Hamaker, Eric Marberg, Atoms for signed permutations, arXiv:1802.09805 [math.CO], 2018.

Crossrefs

Cf. A060854, A074962.

Programs

Mathematica

Table[Product[j!/(n+j)!,{j,0,n}]*(n*(n+1))!,{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+1.

a(n) ~ sqrt(Pi) * exp(n^2/2 + n + 7/12) * n^(n^2 + n + 11/12) / (A * 2^(2*n^2 + 2*n - 1/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 09 2015