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A173048 Triangle T(n, k) = [x^k](p(x, n, q)) where p(x,n,q) = Product_{j=1..n} (x + q^j) + Product_{j=1..n} (x*q^j + 1), p(x, 0, q) = 1, and q = 2, read by rows.

%I A173048 #7 Apr 27 2021 01:04:51
%S A173048 1,3,3,9,12,9,65,70,70,65,1025,990,560,990,1025,32769,31806,11160,
%T A173048 11160,31806,32769,2097153,2064510,671832,178560,671832,2064510,
%U A173048 2097153,268435457,266338558,87413592,12850368,12850368,87413592,266338558,268435457
%N A173048 Triangle T(n, k) = [x^k](p(x, n, q)) where p(x,n,q) = Product_{j=1..n} (x + q^j) + Product_{j=1..n} (x*q^j + 1), p(x, 0, q) = 1, and q = 2, read by rows.
%H A173048 G. C. Greubel, <a href="/A173048/b173048.txt">Rows n = 0..25 of the triangle, flattened</a>
%F A173048 T(n, k) = [x^k](p(x, n, q)) where p(x,n,q) = Product_{j=1..n} (x + q^j) + Product_{j=1..n} (x*q^j + 1), p(x, 0, q) = 1, and q = 2.
%e A173048 Triangle begins as:
%e A173048         1;
%e A173048         3,       3;
%e A173048         9,      12,      9;
%e A173048        65,      70,     70,     65;
%e A173048      1025,     990,    560,    990,   1025;
%e A173048     32769,   31806,  11160,  11160,  31806,   32769;
%e A173048   2097153, 2064510, 671832, 178560, 671832, 2064510, 2097153;
%t A173048 p[x_, n_, q_]:= If[n==0, 1, Product[x+q^j, {j,n}] + Product[x*q^j +1, {j,n}]];
%t A173048 T[n_, k_, q_]:= SeriesCoefficient[p[x,n,q], {x,0,k}];
%t A173048 Table[T[n,k,2], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 26 2021 *)
%o A173048 (Magma)
%o A173048 R<x>:=PowerSeriesRing(Integers(), 50);
%o A173048 p:= func< x,n,q | n eq 0 select 1 else (&*[x+q^j: j in [1..n]]) + (&*[1+q^j*x: j in [1..n]]) >;
%o A173048 T:= func< n,q | Coefficients(R!( p(x,n,q) )) >;
%o A173048 [T(n,2): n in [0..10]]; // _G. C. Greubel_, Apr 26 2021
%Y A173048 Cf. A134058 (q=1), this sequence (q=2), A173049 (q=3).
%K A173048 nonn,tabl,easy,less
%O A173048 0,2
%A A173048 _Roger L. Bagula_, Feb 08 2010
%E A173048 Edited by _G. C. Greubel_, Apr 26 2021