cp's OEIS Frontend

A173505 Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 4, read by rows.

%I A173505 #6 Apr 26 2021 01:54:30
%S A173505 1,1,1,1,3,1,1,45,45,1,1,2835,42525,2835,1,1,722925,683164125,
%T A173505 683164125,722925,1,1,739552275,178213609468125,11227457396491875,
%U A173505 178213609468125,739552275,1,1,3028466566125,746569779579727228125,11993643508948317919828125,11993643508948317919828125,746569779579727228125,3028466566125,1
%N A173505 Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 4, read by rows.
%H A173505 G. C. Greubel, <a href="/A173505/b173505.txt">Rows n = 0..23 of the triangle, flattened</a>
%F A173505 q=4;c(n,q)=Product[(q^m - 1)^(n - m), {m, 1, n}];
%F A173505 t(n,k,q)=c(n, q)/(c(k, q)*c(n - k, q))
%e A173505 The triangle begins as:
%e A173505   1;
%e A173505   1,         1;
%e A173505   1,         3,               1;
%e A173505   1,        45,              45,                 1;
%e A173505   1,      2835,           42525,              2835,               1;
%e A173505   1,    722925,       683164125,         683164125,          722925,         1;
%e A173505   1, 739552275, 178213609468125, 11227457396491875, 178213609468125, 739552275, 1;
%t A173505 c[n_, q_]:= Product[(q^m-1)^(n-m), {m,1,n}];
%t A173505 T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]);
%t A173505 Table[T[n, k, 4], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 25 2021 *)
%o A173505 (Sage)
%o A173505 @CachedFunction
%o A173505 def c(n,q): return product( (q^j -1)^(n-j) for j in (1..n))
%o A173505 def T(n,k,q): return c(n,q)/(c(k,q)*c(n-k,q))
%o A173505 flatten([[T(n,k,4) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, Apr 25 2021
%Y A173505 Cf. A173403, A173404.
%K A173505 nonn,tabl,less
%O A173505 0,5
%A A173505 _Roger L. Bagula_, Feb 20 2010
%E A173505 Edited by _G. C. Greubel_, Apr 25 2021