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A177847
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Array T(n,m)= (n*m)!*Beta(n, m) read by antidiagonals.
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1
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1, 1, 1, 2, 4, 2, 6, 60, 60, 6, 24, 2016, 12096, 2016, 24, 120, 120960, 7983360, 7983360, 120960, 120, 720, 11404800, 12454041600, 149448499200, 12454041600, 11404800, 720, 5040, 1556755200, 38109367296000, 8688935743488000, 8688935743488000
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OFFSET
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1,4
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COMMENTS
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Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y).
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LINKS
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FORMULA
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T(n,m) = Gamma(n*m+1)*Gamma(n)*Gamma(m)/Gamma(n+m).
T(n,m) = T(m,n).
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EXAMPLE
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The array starts in row n=1 as:
1, 1, 2, 6, 24, ...
1, 4, 60, 2016, 120960, ...
2, 60, 12096, 7983360, 12454041600, ...
6, 2016, 7983360, 149448499200, 8688935743488000, ...
24, 120960, 12454041600, 8688935743488000, 24620968322747596800000, ...
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MAPLE
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A177847 := proc(n, m) (n*m)!*Beta(n, m) ; end proc:
seq (seq (A177847(n, 1+d-n), n=1..d), d=1..10);
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MATHEMATICA
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t[n_, m_] = (n*m)!*Beta[n, m];
a = Table[Table[t[n, m], {m, 1, 10}], {n, 1, 10}];
Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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