A174919 A symmetrical triangle sequence:q=3;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, 5, 1, 1, 101, 101, 1, 1, 1297, 15377, 1297, 1, 1, 13457, 1440001, 1440001, 13457, 1, 1, 128165, 120912017, 1146499601, 120912017, 128165, 1, 1, 1179397, 9888711365, 856987141697, 856987141697, 9888711365, 1179397, 1, 1, 10705985

Offset

0,5

Comments

Row sums are:

{1, 2, 7, 204, 17973, 2906918, 1388579967, 1733754064920, 7023953666803081,

77158955191428018954, 2771687022147658804423779,...}.

Links

Table of n, a(n) for n=0..37.

Formula

q=3;

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, 5, 1},
{1, 101, 101, 1},
{1, 1297, 15377, 1297, 1},
{1, 13457, 1440001, 1440001, 13457, 1},
{1, 128165, 120912017, 1146499601, 120912017, 128165, 1},
{1, 1179397, 9888711365, 856987141697, 856987141697, 9888711365, 1179397, 1},
{1, 10705985, 803231797825, 629770267610177, 5762806646575105, 629770267610177, 803231797825, 10705985, 1},
{1, 96668225, 65118185933057, 460319825729437697, 38119092651701970497, 38119092651701970497, 460319825729437697, 65118185933057, 96668225, 1},
{1, 871076197, 5276043118413377, 335868945990739969601, 250778440860581543132225, 2269458391982426259240977, 250778440860581543132225, 335868945990739969601, 5276043118413377, 871076197, 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: A174912 A106238 A173475 * A156952 A158748 A351241

Adjacent sequences: A174916 A174917 A174918 * A174920 A174921 A174922

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved