A174918 A symmetrical triangle sequence:q=2;c(n,q)=Product[(1 - q^i), {i, 1, n}]:t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q))

1, 1, 1, 1, 2, 1, 1, 17, 17, 1, 1, 122, 842, 122, 1, 1, 677, 21026, 21026, 677, 1, 1, 3250, 404497, 1890626, 404497, 3250, 1, 1, 14401, 7001317, 138674177, 138674177, 7001317, 14401, 1, 1, 61010, 115928290, 9428215802, 40287314090, 9428215802

Offset

0,5

Comments

Row sums are:

{1, 2, 4, 36, 1088, 43408, 2706122, 291379792, 59375724296, 23152683334504,

17786745754049930,...}.

Links

Table of n, a(n) for n=0..41.

Formula

q=2;

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

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

Example

{1},
{1, 1},
{1, 2, 1},
{1, 17, 17, 1},
{1, 122, 842, 122, 1},
{1, 677, 21026, 21026, 677, 1},
{1, 3250, 404497, 1890626, 404497, 3250, 1},
{1, 14401, 7001317, 138674177, 138674177, 7001317, 14401, 1},
{1, 61010, 115928290, 9428215802, 40287314090, 9428215802, 115928290, 61010, 1},
{1, 252005, 1883473202, 620866778402, 10953591163642, 10953591163642, 620866778402, 1883473202, 252005, 1},
{1, 1026170, 30347730437, 40291962284026, 2888393566225730, 11929313999517202, 2888393566225730, 40291962284026, 30347730437, 1026170, 1}

Mathematica

Clear[t, n, m, c, q]
c[n_, q_] = Product[(1 - q^i), {i, 1, n}]
t[n_, m_, q_] = 1 + Binomial[n, m]^2 + (c[n, q]/(c[m, q]*c[n - m, q]))^2 - 2*Binomial[n, m]*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: A322621 A309036 A294756 * A154991 A090163 A179071

Adjacent sequences: A174915 A174916 A174917 * A174919 A174920 A174921

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved