A174918 - OEIS

%I #2 Mar 30 2012 17:34:39

%S 1,1,1,1,2,1,1,17,17,1,1,122,842,122,1,1,677,21026,21026,677,1,1,3250,

%T 404497,1890626,404497,3250,1,1,14401,7001317,138674177,138674177,

%U 7001317,14401,1,1,61010,115928290,9428215802,40287314090,9428215802

%N A symmetrical triangle sequence:q=2;c(n,q)=Product[(1 - q^i), {i, 1, n}]:t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q))

%C Row sums are:

%C {1, 2, 4, 36, 1088, 43408, 2706122, 291379792, 59375724296, 23152683334504,

%C 17786745754049930,...}.

%F q=2;

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

%F t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q))

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 17, 17, 1},

%e {1, 122, 842, 122, 1},

%e {1, 677, 21026, 21026, 677, 1},

%e {1, 3250, 404497, 1890626, 404497, 3250, 1},

%e {1, 14401, 7001317, 138674177, 138674177, 7001317, 14401, 1},

%e {1, 61010, 115928290, 9428215802, 40287314090, 9428215802, 115928290, 61010, 1},

%e {1, 252005, 1883473202, 620866778402, 10953591163642, 10953591163642, 620866778402, 1883473202, 252005, 1},

%e {1, 1026170, 30347730437, 40291962284026, 2888393566225730, 11929313999517202, 2888393566225730, 40291962284026, 30347730437, 1026170, 1}

%t Clear[t, n, m, c, q]

%t c[n_, q_] = Product[(1 - q^i), {i, 1, n}]

%t t[n_, m_, q_] = 1 + Binomial[n, m]^2 + (c[n, q]/(c[m, q]*c[n - m, q]))^2 - 2*Binomial[n, m]*c[n, q]/(c[m, q]*c[n - m, q])

%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 02 2010