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

%I A122882 #11 Jul 22 2024 23:30:45
%S A122882 1,2,6,10,6,42,60,20,28,308,390,90,70,154,2310,2652,468,252,308,924,
%T A122882 17556,18564,2652,1092,924,1540,5852,134596,132600,15912,5304,3432,
%U A122882 3960,8360,38456,1038312,961350,99450,27846,14586,12870,18810,48070
%N A122882 Array of T(n,m)=1*5*...*(4n-3)*3*7*...*(4m-1)*2^(n+m)/(n+m)! by antidiagonals.
%C A122882 T(n,m)=2*A(m,n) in Problem A10527 Solution.
%H A122882 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 A122882 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 A122882        1        6       42      308     2310    17556 ...
%e A122882        2        6       28      154      924     5852 ...
%e A122882       10       20       70      308     1540     8360 ...
%e A122882       60       90      252      924     3960    18810 ...
%e A122882      390      468     1092     3432    12870    54340 ...
%e A122882     2652     2652     5304    14586    48620   184756 ...
%e A122882    18564    15912    27846    68068   204204   705432 ...
%e A122882   132600    99450   154700   340340   928200  2939300 ...
%e A122882   961350   640900   897260  1794520  4486300 13113800 ...
%e A122882  7049900  4229940  5383560  9869860 22776600 61822200 ...
%p A122882 A122882 := proc(n,m)
%p A122882     mul(4*i-3,i=1..n)*mul(4*i-1,i=1..m) ;
%p A122882     %*2^(n+m)/(n+m)! ;
%p A122882 end proc: # _R. J. Mathar_, Sep 24 2021
%o A122882 (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 A122882 Cf. A004981(n)=T(n, 0), A004982(n)=T(0, n), A001448(n)=T(n, n).
%K A122882 nonn,tabl,easy
%O A122882 0,2
%A A122882 _Michael Somos_, Sep 16 2006