OFFSET
0,5
COMMENTS
Row sums are:
{1, 2, 12, 652, 136328, 67204536, 159297658162, 1176555717160856,
43519834692800379792, 5103194797279049583074896,
3003810774554741345908169533490,...}.
FORMULA
q=4;
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, 10, 1},
{1, 325, 325, 1},
{1, 6562, 123202, 6562, 1},
{1, 112897, 33489370, 33489370, 112897, 1},
{1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1},
{1, 29746117, 2222580052225, 586055248782085, 586055248782085, 2222580052225, 29746117, 1},
{1, 476854570, 569255746164562, 2405110998912836842, 38708474182528667842, 2405110998912836842, 569255746164562, 476854570, 1},
{1, 7633866385, 145746464523607810, 9856072134501813576226, 2541741180758550820487026, 2541741180758550820487026, 9856072134501813576226, 145746464523607810, 7633866385, 1},
{1, 122160735226, 37312168908143937601, 40375323007070415995666026, 166656597689187698199553355626, 2670416828455727470616462144530, 166656597689187698199553355626, 40375323007070415995666026, 37312168908143937601, 122160735226, 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
KEYWORD
AUTHOR
Roger L. Bagula, Apr 02 2010
STATUS
approved