A122882 Array of T(n,m)=1*5*...*(4n-3)*3*7*...*(4m-1)*2^(n+m)/(n+m)! by antidiagonals.

1, 2, 6, 10, 6, 42, 60, 20, 28, 308, 390, 90, 70, 154, 2310, 2652, 468, 252, 308, 924, 17556, 18564, 2652, 1092, 924, 1540, 5852, 134596, 132600, 15912, 5304, 3432, 3960, 8360, 38456, 1038312, 961350, 99450, 27846, 14586, 12870, 18810, 48070

Offset: 0

Author

Michael Somos, Sep 16 2006

Keywords

• nonn
• tabl
• easy

Comments

T(n,m)=2*A(m,n) in Problem A10527 Solution.

Examples

			       1        6       42      308     2310    17556 ...
       2        6       28      154      924     5852 ...
      10       20       70      308     1540     8360 ...
      60       90      252      924     3960    18810 ...
     390      468     1092     3432    12870    54340 ...
    2652     2652     5304    14586    48620   184756 ...
   18564    15912    27846    68068   204204   705432 ...
  132600    99450   154700   340340   928200  2939300 ...
  961350   640900   897260  1794520  4486300 13113800 ...
 7049900  4229940  5383560  9869860 22776600 61822200 ...
		

Links

• V. Pasol, Problem 10527, Amer. Math. Monthly, 103 (1996), p. 427; Is it an integer: solution to problem 10527, Amer. Math. Monthly, 104 (1997), 980-981.

Crossrefs

Cf. A004981(n)=T(n, 0), A004982(n)=T(0, n), A001448(n)=T(n, n).

Programs

Maple

A122882 := proc(n,m)
    mul(4*i-3,i=1..n)*mul(4*i-1,i=1..m) ;
    %*2^(n+m)/(n+m)! ;
end proc: # R. J. Mathar, Sep 24 2021

PARI

{T(n,m)=if(n<0||m<0, 0, 2^(n+m)/(n+m)!*prod(k=1, m, 4*k-1)*prod(k=1, n, 4*k-3))}

Formula

T(n,m) = T(n,m-1)*(8*m-2)/(n+m) = T(n-1,m)*(8*n-6)/(n+m). T(0,0) = 1.