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

%S 1,1,1,1,4,1,1,37,37,1,1,487,1405,487,1,1,8065,69445,69445,8065,1,1,

%T 163081,4467745,13564261,4467745,163081,1,1,3926881,357799681,

%U 3486035233,3486035233,357799681,3926881,1,1,110058481,34357076641

%N A symmetrical triangle sequence;q=4;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, 6, 76, 2381, 155022, 22825915, 7695523592, 5885796151305,

%C 10048538573544970, 38025550094216572811,...}.

%F q=4;

%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, 4, 1},

%e {1, 37, 37, 1},

%e {1, 487, 1405, 487, 1},

%e {1, 8065, 69445, 69445, 8065, 1},

%e {1, 163081, 4467745, 13564261, 4467745, 163081, 1},

%e {1, 3926881, 357799681, 3486035233, 3486035233, 357799681, 3926881, 1},

%e {1, 110058481, 34357076641, 1116606260881, 3583649359297, 1116606260881, 34357076641, 110058481, 1},

%e {1, 3522839041, 3848216934241, 428879890648801, 4591537656350401, 4591537656350401, 428879890648801, 3848216934241, 3522839041, 1},

%e {1, 126832003201, 492578856806401, 192149735821495201, 7054317360272016001, 23531630490651931201, 7054317360272016001, 192149735821495201, 492578856806401, 126832003201, 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