A177847 Array T(n,m)= (n*m)!*Beta(n, m) read by antidiagonals.

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

Offset: 1

Author

Roger L. Bagula, May 14 2010

Keywords

• nonn
• tabl

Comments

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

Examples

			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, ...
		

Crossrefs

Cf. A060854.

Programs

Maple

A177847 := proc(n,m) (n*m)!*Beta(n,m) ; end proc:
seq (seq (A177847(n, 1+d-n), n=1..d), d=1..10);

Mathematica

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[%]

Formula

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

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

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