_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Apr 17 2010

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]

1, 1, 1, 1, 4, 1, 1, 19, 19, 1, 1, 82, 352, 82, 1, 1, 337, 5788, 5788, 337, 1, 1, 1360, 93079, 376786, 93079, 1360, 1, 1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1, 1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1, 1

0,5

Row sums are:

{1, 2, 6, 40, 518, 12252, 565666, 51409736, 9371059374, 3387887031700,

2463333456291194,...}.

q=4;

c(n,q)=Product[1 - q^i, {i, 1, n}];

t(n,m,q)=t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]

{1},

{1, 1},

{1, 4, 1},

{1, 19, 19, 1},

{1, 82, 352, 82, 1},

{1, 337, 5788, 5788, 337, 1},

{1, 1360, 93079, 376786, 93079, 1360, 1},

{1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1},

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

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

{1, 349516, 6108368761, 6354157930606, 408235958349076, 1634141006295274, 408235958349076, 6354157930606, 6108368761, 349516, 1}

c[n_, q_] = Product[1 - q^i, {i, 1, n}];

t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1;

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 17 2010

approved