A173885 - OEIS

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

%S 1,1,1,1,16,1,1,208,208,1,1,2080,27040,2080,1,1,19360,2516800,2516800,

%T 19360,1,1,176176,213172960,2131729600,213172960,176176,1,1,1591408,

%U 17522993488,1630986316960,1630986316960,17522993488,1591408,1,1

%N Double q-form product triangle:q=3;c(n,q)=Product[(1 - q^i)*(1 - q^(i - 1)), {i, 2, n}];t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q))

%C Row sums are:

%C {1, 2, 18, 418, 31202, 5072322, 2558427874, 3297021803714, 13663552346345922,

%C 151752817493268917122, 5492393089607319374066018,...}.

%F q=3;

%F c(n,q)=Product[(1 - q^i)*(1 - q^(i - 1)), {i, 2, n}];

%F t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q))

%e {1},

%e {1, 1},

%e {1, 16, 1},

%e {1, 208, 208, 1},

%e {1, 2080, 27040, 2080, 1},

%e {1, 19360, 2516800, 2516800, 19360, 1},

%e {1, 176176, 213172960, 2131729600, 213172960, 176176, 1},

%e {1, 1591408, 17522993488, 1630986316960, 1630986316960, 17522993488, 1591408, 1},

%e {1, 14340160, 1426315334080, 1208089087965760, 11244521511065920, 1208089087965760, 1426315334080, 14340160, 1},

%e {1, 129113920, 115719641939200, 885370980476819200, 74990922046386586240, 74990922046386586240, 885370980476819200, 115719641939200, 129113920, 1},

%e {1, 1162182736, 9378373050080320, 646573894604999046400, 494693686762284770400640, 4501712549536791410645824, 494693686762284770400640, 646573894604999046400, 9378373050080320, 1162182736, 1}

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

%t c[n_,q_]=Product[(1-q^i)*(1-q^(i-1)),{i,2,n}];

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

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

%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_, Mar 01 2010