A176427 A symmetrical triangle sequence:q=2;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, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 8, 8, 5, 1, 1, 6, 111, 374, 111, 6, 1, 1, 7, 1041, 8003, 8003, 1041, 7, 1, 1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1, 1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1, 1, 10, 195865, 10491942

Offset

0,5

Comments

Row sums are:

{1, 2, 4, 8, 14, 28, 610, 18104, 471518, 12938116, 419594410,...}.

Links

Table of n, a(n) for n=0..58.

Formula

q=2;

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, 2, 1},
{1, 3, 3, 1},
{1, 4, 4, 4, 1},
{1, 5, 8, 8, 5, 1},
{1, 6, 111, 374, 111, 6, 1},
{1, 7, 1041, 8003, 8003, 1041, 7, 1},
{1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1},
{1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1},
{1, 10, 195865, 10491942, 97749860, 202719054, 97749860, 10491942, 195865, 10, 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: A329330 A049695 A096589 * A324592 A099573 A107430

Adjacent sequences: A176424 A176425 A176426 * A176428 A176429 A176430

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved