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%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,3,1,1,11,11,1,1,37,125,37,1,1,117,1201,1201,117,1,1,359,
%T 10997,33861,10997,359,1,1,1087,99443,925737,925737,99443,1087,1,1,
%U 3273,896233,25095225,75913153,25095225,896233,3273,1,1,9833,8069585
%N A symmetrical triangle sequence;q=3;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]
%C Row sums are:
%C {1, 2, 5, 24, 201, 2638, 56575, 2052536, 127902617, 13721228586, 2544826626411,...}.
%F q=3;
%F c(n,q)=Product[1 - q^i, {i, 1, n}];
%F t(n,m,q)=t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]
%e {1},
%e {1, 1},
%e {1, 3, 1},
%e {1, 11, 11, 1},
%e {1, 37, 125, 37, 1},
%e {1, 117, 1201, 1201, 117, 1},
%e {1, 359, 10997, 33861, 10997, 359, 1},
%e {1, 1087, 99443, 925737, 925737, 99443, 1087, 1},
%e {1, 3273, 896233, 25095225, 75913153, 25095225, 896233, 3273, 1},
%e {1, 9833, 8069585, 678468737, 6174066137, 6174066137, 678468737, 8069585, 9833, 1},
%e {1, 29515, 72636377, 18326727641, 500777835833, 1506472167677, 500777835833, 18326727641, 72636377, 29515, 1}
%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];
%t t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1;
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 17 2010
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