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

0,2

Comments

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

Links

Table of n, a(n) for n=0..42.

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.

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.

Example

       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 ...

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

Prog

(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))}

Crossrefs

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

Sequence in context: A144762 A141572 A141257 * A136700 A054645 A337645

Adjacent sequences: A122879 A122880 A122881 * A122883 A122884 A122885

Keyword

nonn,tabl,easy

Author

Michael Somos, Sep 16 2006

Status

approved