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%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,3,1,1,21,21,1,1,217,497,217,1,1,2785,14401,14401,2785,1,1,
%T 42961,527809,1218961,527809,42961,1,1,781921,23866081,133305985,
%U 133305985,23866081,781921,1,1,16490881,1290574081,18068561281
%N A symmetrical triangle sequence;q=3;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 - n! + n!*c(n, q)/(c[m, q)*c(n - m, q))/Binomial[n, m]
%C Row sums are:
%C {1, 2, 5, 44, 933, 34374, 2360503, 315907976, 82477228041, 41588066488330,
%C 40120217923357451,...}.
%F q=3;
%F c(n,q)=Product[1 - q^i, {i, 1, n}];
%F t(n,m,q)=1 - n! + n!*c(n, q)/(c[m, q)*c(n - m, q))/Binomial[n, m]
%e {1},
%e {1, 1},
%e {1, 3, 1},
%e {1, 21, 21, 1},
%e {1, 217, 497, 217, 1},
%e {1, 2785, 14401, 14401, 2785, 1},
%e {1, 42961, 527809, 1218961, 527809, 42961, 1},
%e {1, 781921, 23866081, 133305985, 133305985, 23866081, 781921, 1},
%e {1, 16490881, 1290574081, 18068561281, 43725975553, 18068561281, 1290574081, 16490881, 1},
%e {1, 396426241, 81341406721, 2930984939521, 17781310471681, 17781310471681, 2930984939521, 81341406721, 396426241, 1},
%e {1, 10710040321, 5857397360641, 554200243833601, 8653441003176961, 21693199214534401, 8653441003176961, 554200243833601, 5857397360641, 10710040321, 1}
%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];
%t t[n_, m_, q_] = 1 - n! + n!*c[n, q]/(c[m, q]*c[n - m, q])/Binomial[n,m];
%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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