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A060855
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Multi-dimensional Catalan numbers: diagonal T(n,n+1) of A060854.
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2
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1, 5, 462, 1662804, 396499770810, 9490348077234178440, 32103104214166146088869942000, 20535535214275361308250745082811167425600, 3201252689605333194364294895470993505956118059617444000
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OFFSET
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1,2
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COMMENTS
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Number of standard tableaux of shape ((n+1)^n). - Emeric Deutsch, May 13 2004
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Product[j!/(n+j)!, {j, 0, n}]*(n*(n+1))!, {n, 1, 10}] (* Vaclav Kotesovec, Mar 09 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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