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A359648 Triangle read by rows. T(n, k) = (n!)^2 / (k! * (n - k)! * (floor(n/2)!)^2 * (floor(n/2) + 1)).

%I A359648 #8 Jan 18 2023 09:34:23
%S A359648 1,1,1,1,2,1,3,9,9,3,2,8,12,8,2,10,50,100,100,50,10,5,30,75,100,75,30,
%T A359648 5,35,245,735,1225,1225,735,245,35,14,112,392,784,980,784,392,112,14,
%U A359648 126,1134,4536,10584,15876,15876,10584,4536,1134,126
%N A359648 Triangle read by rows. T(n, k) = (n!)^2 / (k! * (n - k)! * (floor(n/2)!)^2 * (floor(n/2) + 1)).
%F A359648 T(n, k) = binomial(n, k) * A057977(n).
%e A359648 Triangle T(n, k) starts:
%e A359648 [0]   1;
%e A359648 [1]   1,    1;
%e A359648 [2]   1,    2,    1;
%e A359648 [3]   3,    9,    9,     3;
%e A359648 [4]   2,    8,   12,     8,     2;
%e A359648 [5]  10,   50,  100,   100,    50,    10;
%e A359648 [6]   5,   30,   75,   100,    75,    30,     5;
%e A359648 [7]  35,  245,  735,  1225,  1225,   735,   245,   35;
%e A359648 [8]  14,  112,  392,   784,   980,   784,   392,  112,   14;
%e A359648 [9] 126, 1134, 4536, 10584, 15876, 15876, 10584, 4536, 1134, 126;
%p A359648 T := proc(n, k) n!^2 / (k! * (n - k)! * iquo(n,2)!^2 * (iquo(n,2) + 1)) end:
%p A359648 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%Y A359648 Cf. A057977, A063549, A240558 (row sums), A000007 (alternating row sums).
%K A359648 nonn,tabl
%O A359648 0,5
%A A359648 _Peter Luschny_, Jan 09 2023