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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,10,1,1,325,325,1,1,6562,123202,6562,1,1,112897,33489370,
%T 33489370,112897,1,1,1846882,8663514085,141966936226,8663514085,
%U 1846882,1,1,29746117,2222580052225,586055248782085,586055248782085
%N A symmetrical triangle sequence: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))
%C Row sums are:
%C {1, 2, 12, 652, 136328, 67204536, 159297658162, 1176555717160856,
%C 43519834692800379792, 5103194797279049583074896,
%C 3003810774554741345908169533490,...}.
%F q=4;
%F c(n,q)=Product[(1 - q^i), {i, 1, n}]:
%F 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))
%e {1},
%e {1, 1},
%e {1, 10, 1},
%e {1, 325, 325, 1},
%e {1, 6562, 123202, 6562, 1},
%e {1, 112897, 33489370, 33489370, 112897, 1},
%e {1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1},
%e {1, 29746117, 2222580052225, 586055248782085, 586055248782085, 2222580052225, 29746117, 1},
%e {1, 476854570, 569255746164562, 2405110998912836842, 38708474182528667842, 2405110998912836842, 569255746164562, 476854570, 1},
%e {1, 7633866385, 145746464523607810, 9856072134501813576226, 2541741180758550820487026, 2541741180758550820487026, 9856072134501813576226, 145746464523607810, 7633866385, 1},
%e {1, 122160735226, 37312168908143937601, 40375323007070415995666026, 166656597689187698199553355626, 2670416828455727470616462144530, 166656597689187698199553355626, 40375323007070415995666026, 37312168908143937601, 122160735226, 1}
%t Clear[t, n, m, c, q]
%t c[n_, q_] = Product[(1 - q^i), {i, 1, n}]
%t 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])
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 02 2010
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