A176420 A symmetrical triangle sequence;q=2;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, 2, 1, 1, 5, 5, 1, 1, 12, 30, 12, 1, 1, 27, 146, 146, 27, 1, 1, 58, 637, 1376, 637, 58, 1, 1, 121, 2647, 11777, 11777, 2647, 121, 1, 1, 248, 10768, 97100, 200718, 97100, 10768, 248, 1, 1, 503, 43400, 787952, 3309622, 3309622, 787952, 43400, 503, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, 4, 12, 56, 348, 2768, 29092, 416952, 8282956, 229754592,...}.

Links

Table of n, a(n) for n=0..55.

Formula

q=2;

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, 2, 1},
{1, 5, 5, 1},
{1, 12, 30, 12, 1},
{1, 27, 146, 146, 27, 1},
{1, 58, 637, 1376, 637, 58, 1},
{1, 121, 2647, 11777, 11777, 2647, 121, 1},
{1, 248, 10768, 97100, 200718, 97100, 10768, 248, 1},
{1, 503, 43400, 787952, 3309622, 3309622, 787952, 43400, 503, 1},
{1, 1014, 174207, 6347596, 53743778, 109221400, 53743778, 6347596, 174207, 1014, 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: A197090 A008518 A264862 * A099927 A139332 A187617

Adjacent sequences: A176417 A176418 A176419 * A176421 A176422 A176423

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved