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Array T(n,m)= (n*m)!*Beta(n, m) read by antidiagonals.
1

%I #7 Aug 06 2012 20:22:50

%S 1,1,1,2,4,2,6,60,60,6,24,2016,12096,2016,24,120,120960,7983360,

%T 7983360,120960,120,720,11404800,12454041600,149448499200,12454041600,

%U 11404800,720,5040,1556755200,38109367296000,8688935743488000,8688935743488000

%N Array T(n,m)= (n*m)!*Beta(n, m) read by antidiagonals.

%C Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y).

%F T(n,m) = Gamma(n*m+1)*Gamma(n)*Gamma(m)/Gamma(n+m).

%F T(1,m) = A000142(m-1).

%F T(n,m) = T(m,n).

%e The array starts in row n=1 as:

%e 1, 1, 2, 6, 24, ...

%e 1, 4, 60, 2016, 120960, ...

%e 2, 60, 12096, 7983360, 12454041600, ...

%e 6, 2016, 7983360, 149448499200, 8688935743488000, ...

%e 24, 120960, 12454041600, 8688935743488000, 24620968322747596800000, ...

%p A177847 := proc(n,m) (n*m)!*Beta(n,m) ; end proc:

%p seq (seq (A177847(n, 1+d-n), n=1..d), d=1..10);

%t t[n_, m_] = (n*m)!*Beta[n, m];

%t a = Table[Table[t[n, m], {m, 1, 10}], {n, 1, 10}];

%t Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];

%t Flatten[%]

%Y Cf. A060854.

%K nonn,tabl

%O 1,4

%A _Roger L. Bagula_, May 14 2010