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A131429 Triangle read by rows: T(n,k) = C(n) + C(k) - 1 where C(n) = A000108(n) are the Catalan numbers, 0 <= k <= n.

%I A131429 #9 Sep 01 2018 21:28:55
%S A131429 1,1,1,2,2,3,5,5,6,9,14,14,15,18,27,42,42,43,46,55,83,132,132,133,136,
%T A131429 145,173,263,429,429,430,433,442,470,560,857,1430,1430,1431,1434,1443,
%U A131429 1471,1561,1858,2859,4862,4862,4863,4866,4875,4903,4993,5290,6291,9723
%N A131429 Triangle read by rows: T(n,k) = C(n) + C(k) - 1 where C(n) = A000108(n) are the Catalan numbers, 0 <= k <= n.
%C A131429 Left column = Catalan numbers, A000108. Right border = 2*A000108 - 1. Row sums = A131430: (1, 2, 7, 25, 88, 311, 1114, ...).
%H A131429 Andrew Howroyd, <a href="/A131429/b131429.txt">Table of n, a(n) for n = 0..1274</a> (first 50 rows)
%F A131429 Equals (A000012 * A131427) + (A131427 * A000012) - A000012 as infinite lower triangular matrices.
%e A131429 First few rows of the triangle are:
%e A131429    1;
%e A131429    1,  1;
%e A131429    2,  2,  3;
%e A131429    5,  5,  6,  9;
%e A131429   14, 14, 15, 18, 27;
%e A131429   42, 42, 43, 46, 55, 83;
%e A131429   ...
%o A131429 (PARI) T(n,k)=if(k<=n, binomial(2*n,n)/(n+1) + binomial(2*k,k)/(k+1) - 1, 0) \\ _Andrew Howroyd_, Sep 01 2018
%Y A131429 Column k=0 is A000108.
%Y A131429 Row sums are A131430.
%Y A131429 Cf. A131427, A131428.
%K A131429 nonn,tabl
%O A131429 0,4
%A A131429 _Gary W. Adamson_, Jul 10 2007
%E A131429 Name clarified by _Andrew Howroyd_, Sep 01 2018