A173885 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))

1, 1, 1, 1, 16, 1, 1, 208, 208, 1, 1, 2080, 27040, 2080, 1, 1, 19360, 2516800, 2516800, 19360, 1, 1, 176176, 213172960, 2131729600, 213172960, 176176, 1, 1, 1591408, 17522993488, 1630986316960, 1630986316960, 17522993488, 1591408, 1, 1

Offset

0,5

Comments

Row sums are:

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

151752817493268917122, 5492393089607319374066018,...}.

Links

Table of n, a(n) for n=0..36.

Formula

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))

Example

{1},
{1, 1},
{1, 16, 1},
{1, 208, 208, 1},
{1, 2080, 27040, 2080, 1},
{1, 19360, 2516800, 2516800, 19360, 1},
{1, 176176, 213172960, 2131729600, 213172960, 176176, 1},
{1, 1591408, 17522993488, 1630986316960, 1630986316960, 17522993488, 1591408, 1},
{1, 14340160, 1426315334080, 1208089087965760, 11244521511065920, 1208089087965760, 1426315334080, 14340160, 1},
{1, 129113920, 115719641939200, 885370980476819200, 74990922046386586240, 74990922046386586240, 885370980476819200, 115719641939200, 129113920, 1},
{1, 1162182736, 9378373050080320, 646573894604999046400, 494693686762284770400640, 4501712549536791410645824, 494693686762284770400640, 646573894604999046400, 9378373050080320, 1162182736, 1}

Mathematica

Clear[t, n, m, c, q];
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]);
Table[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 2, 12}];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

Crossrefs

Sequence in context: A142462 A203397 A338029 * A173585 A022179 A015141

Adjacent sequences: A173882 A173883 A173884 * A173886 A173887 A173888

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 01 2010

Status

approved