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A173507 Triangle T(n, k, q) = 2*c(n, q)/(c(k,q)*c(n-k,q)) where c(n,q) = Product_{j=0..n} (q^(q^j) - 1) and q=3, read by rows.

%I A173507 #12 Apr 28 2021 01:58:04
%S A173507 1,1,1,1,757,1,1,293292210961,293292210961,1,1,
%T A173507 17054864932424529613394216562274995877,
%U A173507 6607739819910193062857078382087289676159166721,17054864932424529613394216562274995877,1
%N A173507 Triangle T(n, k, q) = 2*c(n, q)/(c(k,q)*c(n-k,q)) where c(n,q) = Product_{j=0..n} (q^(q^j) - 1) and q=3, read by rows.
%H A173507 G. C. Greubel, <a href="/A173507/b173507.txt">Rows n = 0..7 of the triangle, flattened</a>
%F A173507 T(n, k, q) = 2*c(n, q)/(c(k,q)*c(n-k,q)) where c(n,q) = Product_{j=0..n} (q^(q^j) - 1) and q=3.
%e A173507 The triangle begins as:
%e A173507   1;
%e A173507   1,            1;
%e A173507   1,          757,            1;
%e A173507   1, 293292210961, 293292210961, 1;
%t A173507 c[n_, q_]:= Product[q^(q^j) -1, {j,0,n}];
%t A173507 T[n_, k_, q_]:= 2*c[n, q]/(c[k, q]*c[n-k, q]);
%t A173507 Table[T[n, k, 3], {n, 0, 6}, {k, 0, n}]//Flatten (* modified by _G. C. Greubel_, Apr 25 2021 *)
%o A173507 (Sage)
%o A173507 @CachedFunction
%o A173507 def c(n,q): return product(q^(q^j) -1 for j in (0..n))
%o A173507 def T(n,k,q): return 2*c(n,q)/(c(k,q)*c(n-k,q))
%o A173507 flatten([[T(n,k,3) for k in (0..n)] for n in (0..6)]) # _G. C. Greubel_, Apr 25 2021
%K A173507 nonn,tabl,easy,less
%O A173507 0,5
%A A173507 _Roger L. Bagula_, Feb 20 2010
%E A173507 Edited by _G. C. Greubel_, Apr 25 2021