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%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,2,1,1,5,5,1,1,12,30,12,1,1,27,146,146,27,1,1,58,637,1376,637,
%T 58,1,1,121,2647,11777,11777,2647,121,1,1,248,10768,97100,200718,
%U 97100,10768,248,1,1,503,43400,787952,3309622,3309622,787952,43400,503,1,1
%N A symmetrical triangle sequence;q=2;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, 4, 12, 56, 348, 2768, 29092, 416952, 8282956, 229754592,...}.
%F q=2;
%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, 2, 1},
%e {1, 5, 5, 1},
%e {1, 12, 30, 12, 1},
%e {1, 27, 146, 146, 27, 1},
%e {1, 58, 637, 1376, 637, 58, 1},
%e {1, 121, 2647, 11777, 11777, 2647, 121, 1},
%e {1, 248, 10768, 97100, 200718, 97100, 10768, 248, 1},
%e {1, 503, 43400, 787952, 3309622, 3309622, 787952, 43400, 503, 1},
%e {1, 1014, 174207, 6347596, 53743778, 109221400, 53743778, 6347596, 174207, 1014, 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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