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A379100 Triangle read by rows: T(n, k) = binomial(2*k, k) * binomial(2*n, n) / (n + 1).

%I A379100 #8 Dec 15 2024 11:01:43
%S A379100 1,1,2,2,4,12,5,10,30,100,14,28,84,280,980,42,84,252,840,2940,10584,
%T A379100 132,264,792,2640,9240,33264,121968,429,858,2574,8580,30030,108108,
%U A379100 396396,1472328,1430,2860,8580,28600,100100,360360,1321320,4907760,18404100
%N A379100 Triangle read by rows: T(n, k) = binomial(2*k, k) * binomial(2*n, n) / (n + 1).
%F A379100 T(n, k) = ((2*k)! * (2*n)!) / ((k! * n!)^2 * (n+1)).
%e A379100   [0]   1;
%e A379100   [1]   1,   2;
%e A379100   [2]   2,   4,   12;
%e A379100   [3]   5,  10,   30,  100;
%e A379100   [4]  14,  28,   84,  280,   980;
%e A379100   [5]  42,  84,  252,  840,  2940,  10584;
%e A379100   [6] 132, 264,  792, 2640,  9240,  33264, 121968;
%e A379100   [7] 429, 858, 2574, 8580, 30030, 108108, 396396, 1472328;
%p A379100 T := (n, k) -> binomial(2*k, k) * binomial(2*n, n) / (n + 1):
%p A379100 seq(seq(T(n, k), k = 0..n), n = 0..8);
%Y A379100 Cf. A002894, A000888, A270577, A379099 (row sums).
%K A379100 nonn,tabl
%O A379100 0,3
%A A379100 _Peter Luschny_, Dec 15 2024