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A132752 Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows.

%I A132752 #5 Feb 16 2021 17:48:48
%S A132752 1,3,1,3,3,1,3,5,5,1,3,7,11,7,1,3,9,19,19,9,1,3,11,29,39,29,11,1,3,13,
%T A132752 41,69,69,41,13,1,3,15,55,111,139,111,55,15,1,3,17,71,167,251,251,167,
%U A132752 71,17,1
%N A132752 Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows.
%H A132752 G. C. Greubel, <a href="/A132752/b132752.txt">Rows n = 0..100 of the triangle, flattened</a>
%F A132752 T(n, k) = 2*A132749(n, k) - 1, an infinite lower triangular matrix.
%F A132752 From _G. C. Greubel_, Feb 16 2021: (Start)
%F A132752 T(n, k) = A109128(n, k) with T(n, 0) = 3.
%F A132752 Sum_{k=0..n} T(n, k) = 2^(n+1) -n +1 -2*[n=0] = A132753(n) - 2*[n=0]. (End)
%e A132752 First few rows of the triangle are:
%e A132752   1;
%e A132752   3,  1;
%e A132752   3,  3,  1;
%e A132752   3,  5,  5,  1;
%e A132752   3,  7, 11,  7,  1;
%e A132752   3,  9, 19, 19,  9,  1;
%e A132752   3, 11, 29, 39, 29, 11, 1;
%e A132752   ...
%t A132752 T[n_, k_]:= If[k==n, 1, If[k==0, 3, 2*Binomial[n, k] -1 ]];
%t A132752 Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Feb 16 2021 *)
%o A132752 (Sage)
%o A132752 def A132752(n,k): return 1 if k==n else 3 if k==0 else 2*binomial(n,k) -1
%o A132752 flatten([[A132752(n,k) for k in [0..n]] for n in [0..12]]) # _G. C. Greubel_, Feb 16 2021
%o A132752 (Magma)
%o A132752 A132752:= func< n,k | k eq n select 1 else k eq 0 select 3 else 2*Binomial(n,k) -1 >;
%o A132752 [A132752(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Feb 16 2021
%Y A132752 Cf. A109128, A132749, A132753.
%K A132752 nonn,tabl
%O A132752 0,2
%A A132752 _Gary W. Adamson_, Aug 28 2007