A174919 - OEIS

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

%S 1,1,1,1,5,1,1,101,101,1,1,1297,15377,1297,1,1,13457,1440001,1440001,

%T 13457,1,1,128165,120912017,1146499601,120912017,128165,1,1,1179397,

%U 9888711365,856987141697,856987141697,9888711365,1179397,1,1,10705985

%N A symmetrical triangle sequence:q=3;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, 7, 204, 17973, 2906918, 1388579967, 1733754064920, 7023953666803081,

%C 77158955191428018954, 2771687022147658804423779,...}.

%F q=3;

%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, 5, 1},

%e {1, 101, 101, 1},

%e {1, 1297, 15377, 1297, 1},

%e {1, 13457, 1440001, 1440001, 13457, 1},

%e {1, 128165, 120912017, 1146499601, 120912017, 128165, 1},

%e {1, 1179397, 9888711365, 856987141697, 856987141697, 9888711365, 1179397, 1},

%e {1, 10705985, 803231797825, 629770267610177, 5762806646575105, 629770267610177, 803231797825, 10705985, 1},

%e {1, 96668225, 65118185933057, 460319825729437697, 38119092651701970497, 38119092651701970497, 460319825729437697, 65118185933057, 96668225, 1},

%e {1, 871076197, 5276043118413377, 335868945990739969601, 250778440860581543132225, 2269458391982426259240977, 250778440860581543132225, 335868945990739969601, 5276043118413377, 871076197, 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