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A171534 Triangle read by rows: T(n,k)=binomial(2*n*k+k,2)/(2*n+1).

%I A171534 #2 Mar 30 2012 17:34:36
%S A171534 1,2,9,3,13,30,4,17,39,70,5,21,48,86,135,6,25,57,102,160,231,7,29,66,
%T A171534 118,185,267,364,8,33,75,134,210,303,413,540,9,37,84,150,235,339,462,
%U A171534 604,765,10,41,93,166,260,375,511,668,846,104
%N A171534 Triangle read by rows: T(n,k)=binomial(2*n*k+k,2)/(2*n+1).
%C A171534 Row sums are: 1, 11, 46, 130, 295, 581, 1036, 1716, 2685, 4015,... see A006324
%D A171534 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 145.
%F A171534 T(n,k)=binomial(2*n*k + k, 2)/(2*n + 1).
%e A171534 1;
%e A171534 2, 9;
%e A171534 3, 13, 30;
%e A171534 4, 17, 39, 70;
%e A171534 5, 21, 48, 86, 135;
%e A171534 6, 25, 57, 102, 160, 231;
%e A171534 7, 29, 66, 118, 185, 267, 364;
%e A171534 8, 33, 75, 134, 210, 303, 413, 540;
%e A171534 9, 37, 84, 150, 235, 339, 462, 604, 765;
%e A171534 10, 41, 93, 166, 260, 375, 511, 668, 846, 1045;
%t A171534 Table[Table[Binomial[2*n*k + k, 2]/(2*n + 1), {k, 1, n}], {n, 1, 10}]
%t A171534 Flatten[%]
%Y A171534 Cf. A008406
%K A171534 nonn,tabl
%O A171534 1,2
%A A171534 _Roger L. Bagula_, Dec 11 2009
%E A171534 Introduced OEIS notational standards and keyword:tabl - The Assoc. Editors of the OEIS, Dec 15 2009