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%I #22 Apr 13 2014 13:48:56
%S 1,1,4,1,6,15,1,8,28,56,1,10,45,120,210,1,12,66,220,495,792,1,14,91,
%T 364,1001,2002,3003,1,16,120,560,1820,4368,8008,11440,1,18,153,816,
%U 3060,8568,18564,31824,43758,1,20,190
%N Triangle read by rows: T(n,k) (0 <= k <= n) = binomial(2*n+2,k).
%C Row sums are A000346.
%H Roger L. Bagula, <a href="/A225419/a225419.txt">a225419nb.txt</a>
%e Triangle begins:
%e 1,
%e 1, 4,
%e 1, 6, 15,
%e 1, 8, 28, 56,
%e 1, 10, 45, 120, 210,
%e 1, 12, 66, 220, 495, 792,
%e 1, 14, 91, 364, 1001, 2002, 3003,
%e ...
%t Flatten[Table[Table[DifferenceRoot[Function[{y, n}, {(-(2*m + 1) + n) y[n] + n y[1 + n] == 0, y[1] == 1}]][k], {k, 1, m}], {m, 1, 10}]]
%t Flatten[Table[Binomial[2n+2,k],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Apr 13 2014 *)
%Y Cf. A127673, A062344, A034870, A000346.
%K nonn,tabl,easy
%O 0,3
%A _Roger L. Bagula_, May 07 2013
%E Edited by _N. J. A. Sloane_, May 11 2013
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