A176429 A symmetrical triangle sequence:q=4;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, 6, 1, 1, 31, 31, 1, 1, 144, 648, 144, 1, 1, 625, 11292, 11292, 625, 1, 1, 2610, 184995, 751194, 184995, 2610, 1, 1, 10675, 2977413, 48401607, 48401607, 2977413, 10675, 1, 1, 43188, 47703610, 3101595936, 12443070892, 3101595936, 47703610

Offset

0,5

Comments

Row sums are:

{1, 2, 8, 64, 938, 23836, 1126406, 102779392, 18741756362, 6775770435604,

4926666872667614,...}.

Links

Table of n, a(n) for n=0..42.

Formula

q=4;

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, 6, 1},
{1, 31, 31, 1},
{1, 144, 648, 144, 1},
{1, 625, 11292, 11292, 625, 1},
{1, 2610, 184995, 751194, 184995, 2610, 1},
{1, 10675, 2977413, 48401607, 48401607, 2977413, 10675, 1},
{1, 43188, 47703610, 3101595936, 12443070892, 3101595936, 47703610, 43188, 1},
{1, 173749, 763487338, 198555049906, 3188566506808, 3188566506808, 198555049906, 763487338, 173749, 1},
{1, 697014, 12216584973, 12708313657962, 816471906960456, 3268281996866802, 816471906960456, 12708313657962, 12216584973, 697014, 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: A174186 A111578 A166349 * A157155 A022169 A156601

Adjacent sequences: A176426 A176427 A176428 * A176430 A176431 A176432

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved