A173884 Double q-form product triangle:q=2;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, 3, 1, 1, 21, 21, 1, 1, 105, 735, 105, 1, 1, 465, 16275, 16275, 465, 1, 1, 1953, 302715, 1513575, 302715, 1953, 1, 1, 8001, 5208651, 115334415, 115334415, 5208651, 8001, 1, 1, 32385, 86370795, 8032483935, 35572428855, 8032483935

Offset

0,5

Comments

Row sums are:

{1, 2, 5, 44, 947, 33482, 2122913, 241102136, 51810203087, 21011300238182,

16612823490798845,...}.

Links

Table of n, a(n) for n=0..41.

Formula

q=2;

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, 3, 1},
{1, 21, 21, 1},
{1, 105, 735, 105, 1},
{1, 465, 16275, 16275, 465, 1},
{1, 1953, 302715, 1513575, 302715, 1953, 1},
{1, 8001, 5208651, 115334415, 115334415, 5208651, 8001, 1},
{1, 32385, 86370795, 8032483935, 35572428855, 8032483935, 86370795, 32385, 1},
{1, 130305, 1406642475, 535930782975, 9968312563335, 9968312563335, 535930782975, 1406642475, 130305, 1},
{1, 522753, 22705776555, 35015551130175, 2668184996119335, 11206376983701207, 2668184996119335, 35015551130175, 22705776555, 522753, 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: A212855 A016561 A111382 * A176418 A156950 A083998

Adjacent sequences: A173881 A173882 A173883 * A173885 A173886 A173887

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 01 2010

Status

approved