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%I #3 Mar 30 2012 18:36:58
%S 1,2,1,10,4,1,84,28,7,1,1001,286,66,11,1,15504,3876,816,136,16,1,
%T 296010,65780,12650,2024,253,22,1,6724520,1344904,237336,35960,4495,
%U 435,29,1,177232627,32224114,5245786,749398,91390,9139,703,37,1,5317936260
%N Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k, n-k), for n>=k>=0.
%C A triangle having similar properties and complementary construction is the dual triangle A122175.
%F Remarkably, row n of the matrix inverse (A121439) equals row n of A121412^(-n*(n+1)/2-1). Further, the following matrix products of triangles of binomial coefficients are equal: A121412 = A121334*A122178^-1 = A121335*A121334^-1 = A121336*A121335^-1, where row n of H=A121412 equals row (n-1) of H^(n+1) with an appended '1'.
%e Triangle begins:
%e 1;
%e 2, 1;
%e 10, 4, 1;
%e 84, 28, 7, 1;
%e 1001, 286, 66, 11, 1;
%e 15504, 3876, 816, 136, 16, 1;
%e 296010, 65780, 12650, 2024, 253, 22, 1;
%e 6724520, 1344904, 237336, 35960, 4495, 435, 29, 1;
%e 177232627, 32224114, 5245786, 749398, 91390, 9139, 703, 37, 1; ...
%o (PARI) T(n,k)=binomial(n*(n+1)/2+n-k,n-k)
%Y Cf. A121439 (matrix inverse); A121412; variants: A122178, A121335, A121336; A122175 (dual).
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Aug 29 2006
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