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

1,4

Comments

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

Links

Table of n, a(n) for n=1..33.

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).

Example

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, ...

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[%]

Crossrefs

Cf. A060854.

Sequence in context: A154120 A361727 A261964 * A296471 A021416 A094756

Adjacent sequences: A177844 A177845 A177846 * A177848 A177849 A177850

Keyword

nonn,tabl

Author

Roger L. Bagula, May 14 2010

Status

approved