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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,3,1,1,21,21,1,1,105,735,105,1,1,465,16275,16275,465,1,1,1953,
%T 302715,1513575,302715,1953,1,1,8001,5208651,115334415,115334415,
%U 5208651,8001,1,1,32385,86370795,8032483935,35572428855,8032483935
%N Double q-form product triangle:q=2;c(n,q)=Product[(1 - q^i)*(1 - q^(i - 1)), {i, 2, n}];t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q))
%C Row sums are:
%C {1, 2, 5, 44, 947, 33482, 2122913, 241102136, 51810203087, 21011300238182,
%C 16612823490798845,...}.
%F q=2;
%F c(n,q)=Product[(1 - q^i)*(1 - q^(i - 1)), {i, 2, n}];
%F t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q))
%e {1},
%e {1, 1},
%e {1, 3, 1},
%e {1, 21, 21, 1},
%e {1, 105, 735, 105, 1},
%e {1, 465, 16275, 16275, 465, 1},
%e {1, 1953, 302715, 1513575, 302715, 1953, 1},
%e {1, 8001, 5208651, 115334415, 115334415, 5208651, 8001, 1},
%e {1, 32385, 86370795, 8032483935, 35572428855, 8032483935, 86370795, 32385, 1},
%e {1, 130305, 1406642475, 535930782975, 9968312563335, 9968312563335, 535930782975, 1406642475, 130305, 1},
%e {1, 522753, 22705776555, 35015551130175, 2668184996119335, 11206376983701207, 2668184996119335, 35015551130175, 22705776555, 522753, 1}
%t Clear[t,n,m,c,q];
%t c[n_,q_]=Product[(1-q^i)*(1-q^(i-1)),{i,2,n}];
%t t[n_,m_,q_]=c[n,q]/(c[m,q]*c[n-m,q]);
%t Table[Table[Table[t[n,m,q],{m,0,n}],{n,0,10}],{q,2,12}];
%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_, Mar 01 2010
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