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A381883 Triangle read by rows: T(n, k) = binomial(2*n - 1, k).

%I A381883 #10 Apr 03 2025 09:58:47
%S A381883 1,1,1,1,3,3,1,5,10,10,1,7,21,35,35,1,9,36,84,126,126,1,11,55,165,330,
%T A381883 462,462,1,13,78,286,715,1287,1716,1716,1,15,105,455,1365,3003,5005,
%U A381883 6435,6435,1,17,136,680,2380,6188,12376,19448,24310,24310
%N A381883 Triangle read by rows: T(n, k) = binomial(2*n - 1, k).
%e A381883 Triangle starts:
%e A381883   [0] 1;
%e A381883   [1] 1,  1;
%e A381883   [2] 1,  3,   3;
%e A381883   [3] 1,  5,  10,  10;
%e A381883   [4] 1,  7,  21,  35,   35;
%e A381883   [5] 1,  9,  36,  84,  126,  126;
%e A381883   [6] 1, 11,  55, 165,  330,  462,  462;
%e A381883   [7] 1, 13,  78, 286,  715, 1287, 1716, 1716;
%e A381883   [8] 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435;
%p A381883 T := (n, k) -> binomial(2*n - 1, k):
%p A381883 seq(seq(T(n, k), k = 0..n), n = 0..9);
%t A381883 T[n_,k_]:=Binomial[2n-1,k];Table[T[n,k],{n,0,9},{k,0,n}]//Flatten (* _James C. McMahon_, Apr 02 2025 *)
%Y A381883 Cf. A007318 (Pascal), A088218 (main diagonal), A114121 (row sums), A262977 (central terms).
%K A381883 nonn,tabl,easy
%O A381883 0,5
%A A381883 _Peter Luschny_, Mar 15 2025