A176421 A symmetrical triangle sequence;q=3;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]

1, 1, 1, 1, 3, 1, 1, 11, 11, 1, 1, 37, 125, 37, 1, 1, 117, 1201, 1201, 117, 1, 1, 359, 10997, 33861, 10997, 359, 1, 1, 1087, 99443, 925737, 925737, 99443, 1087, 1, 1, 3273, 896233, 25095225, 75913153, 25095225, 896233, 3273, 1, 1, 9833, 8069585

Offset

0,5

Comments

Row sums are:

{1, 2, 5, 24, 201, 2638, 56575, 2052536, 127902617, 13721228586, 2544826626411,...}.

Links

Table of n, a(n) for n=0..47.

Formula

q=3;

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

t(n,m,q)=t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]

Example

{1},
{1, 1},
{1, 3, 1},
{1, 11, 11, 1},
{1, 37, 125, 37, 1},
{1, 117, 1201, 1201, 117, 1},
{1, 359, 10997, 33861, 10997, 359, 1},
{1, 1087, 99443, 925737, 925737, 99443, 1087, 1},
{1, 3273, 896233, 25095225, 75913153, 25095225, 896233, 3273, 1},
{1, 9833, 8069585, 678468737, 6174066137, 6174066137, 678468737, 8069585, 9833, 1},
{1, 29515, 72636377, 18326727641, 500777835833, 1506472167677, 500777835833, 18326727641, 72636377, 29515, 1}

Mathematica

c[n_, q_] = Product[1 - q^i, {i, 1, n}];
t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

Crossrefs

Sequence in context: A013561 A348211 A176468 * A168552 A111473 A234944

Adjacent sequences: A176418 A176419 A176420 * A176422 A176423 A176424

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved