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A177847 Array T(n,m)= (n*m)!*Beta(n, m) read by antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A229460 A154120 A261964 * A296471 A021416 A094756

Adjacent sequences:  A177844 A177845 A177846 * A177848 A177849 A177850

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, May 14 2010

STATUS

approved

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)