A176428 A symmetrical triangle sequence:q=3;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

1, 1, 1, 1, 4, 1, 1, 15, 15, 1, 1, 54, 194, 54, 1, 1, 185, 2118, 2118, 185, 1, 1, 608, 20831, 65344, 20831, 608, 1, 1, 1939, 194633, 1835923, 1835923, 194633, 1939, 1, 1, 6058, 1777912, 50102326, 151670254, 50102326, 1777912, 6058, 1, 1, 18669, 16091400

Offset

0,5

Comments

Row sums are:

{1, 2, 6, 32, 304, 4608, 108224, 4064992, 255442848, 27438829376, 5089613338048,...}.

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)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

Example

{1},
{1, 1},
{1, 4, 1},
{1, 15, 15, 1},
{1, 54, 194, 54, 1},
{1, 185, 2118, 2118, 185, 1},
{1, 608, 20831, 65344, 20831, 608, 1},
{1, 1939, 194633, 1835923, 1835923, 194633, 1939, 1},
{1, 6058, 1777912, 50102326, 151670254, 50102326, 1777912, 6058, 1},
{1, 18669, 16091400, 1356482448, 12346822170, 12346822170, 1356482448, 16091400, 18669, 1},
{1, 57012, 145120205, 36651252032, 1001545933970, 3012928611608, 1001545933970, 36651252032, 145120205, 57012, 1}

Mathematica

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

Crossrefs

Sequence in context: A320280 A343804 A157211 * A116469 A156599 A010320

Adjacent sequences: A176425 A176426 A176427 * A176429 A176430 A176431

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved