A176422 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,4,1,1,19,19,1,1,82,352,82,1,1,337,5788,5788,337,1,1,1360,

%T 93079,376786,93079,1360,1,1,5455,1490833,24208579,24208579,1490833,

%U 5455,1,1,21838,23859082,1550842030,6221613472,1550842030,23859082,21838,1,1

%N A symmetrical triangle sequence;q=4;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, 6, 40, 518, 12252, 565666, 51409736, 9371059374, 3387887031700,

%C 2463333456291194,...}.

%F q=4;

%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, 4, 1},

%e {1, 19, 19, 1},

%e {1, 82, 352, 82, 1},

%e {1, 337, 5788, 5788, 337, 1},

%e {1, 1360, 93079, 376786, 93079, 1360, 1},

%e {1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1},

%e {1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1},

%e {1, 87373, 381767554, 99277752466, 1594283908456, 1594283908456, 99277752466, 381767554, 87373, 1},

%e {1, 349516, 6108368761, 6354157930606, 408235958349076, 1634141006295274, 408235958349076, 6354157930606, 6108368761, 349516, 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