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 A060855 Multi-dimensional Catalan numbers: diagonal T(n,n+1) of A060854. 2
 1, 5, 462, 1662804, 396499770810, 9490348077234178440, 32103104214166146088869942000, 20535535214275361308250745082811167425600, 3201252689605333194364294895470993505956118059617444000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. 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 MATHEMATICA Table[Product[j!/(n+j)!, {j, 0, n}]*(n*(n+1))!, {n, 1, 10}] (* Vaclav Kotesovec, Mar 09 2015 *) CROSSREFS Sequence in context: A332145 A144509 A240700 * A212043 A182403 A125534 Adjacent sequences:  A060852 A060853 A060854 * A060856 A060857 A060858 KEYWORD nonn,easy AUTHOR R. H. Hardin, May 03 2001 STATUS approved

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Last modified October 1 03:36 EDT 2020. Contains 337441 sequences. (Running on oeis4.)