A122882 - OEIS

%I #11 Jul 22 2024 23:30:45

%S 1,2,6,10,6,42,60,20,28,308,390,90,70,154,2310,2652,468,252,308,924,

%T 17556,18564,2652,1092,924,1540,5852,134596,132600,15912,5304,3432,

%U 3960,8360,38456,1038312,961350,99450,27846,14586,12870,18810,48070

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

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

%H V. Pasol, <a href="https://www.jstor.org/stable/2974937">Problem 10527</a>, Amer. Math. Monthly, 103 (1996), p. 427; <a href="https://www.jstor.org/stable/2974489">Is it an integer: solution to problem 10527</a>, Amer. Math. Monthly, 104 (1997), 980-981.

%F 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.

%e        1        6       42      308     2310    17556 ...

%e        2        6       28      154      924     5852 ...

%e       10       20       70      308     1540     8360 ...

%e       60       90      252      924     3960    18810 ...

%e      390      468     1092     3432    12870    54340 ...

%e     2652     2652     5304    14586    48620   184756 ...

%e    18564    15912    27846    68068   204204   705432 ...

%e   132600    99450   154700   340340   928200  2939300 ...

%e   961350   640900   897260  1794520  4486300 13113800 ...

%e  7049900  4229940  5383560  9869860 22776600 61822200 ...

%p A122882 := proc(n,m)

%p     mul(4*i-3,i=1..n)*mul(4*i-1,i=1..m) ;

%p     %*2^(n+m)/(n+m)! ;

%p end proc: # _R. J. Mathar_, Sep 24 2021

%o (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))}

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

%K nonn,tabl,easy

%O 0,2

%A _Michael Somos_, Sep 16 2006