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A228035 Triangle T(n,k), read by rows: T(n,k) is the denominator of (1-2^(n-k+1))/(1-2^(k+1)).

%I A228035 #26 Sep 08 2022 08:46:05
%S A228035 1,1,3,1,1,7,1,3,7,15,1,1,1,5,31,1,3,7,15,31,63,1,1,7,1,31,21,127,1,3,
%T A228035 1,15,31,9,127,255,1,1,7,5,1,21,127,85,511,1,3,7,15,31,63,127,255,511,
%U A228035 1023,1,1,1,1,31,1,127,17,73,341,2047,1,3,7,15,31,63
%N A228035 Triangle T(n,k), read by rows: T(n,k) is the denominator of (1-2^(n-k+1))/(1-2^(k+1)).
%C A228035 The numerators are given in A227984.
%C A228035 The first diagonal is A000225, the second diagonal is A213243, the third diagonal is A213245.
%H A228035 Vincenzo Librandi, <a href="/A228035/b228035.txt">Rows n = 0..100, flattened</a>
%e A228035 Triangle begins:
%e A228035 1;
%e A228035 1, 3;
%e A228035 1, 1, 7;
%e A228035 1, 3, 7, 15;
%e A228035 1, 1, 1, 5,  31;
%e A228035 1, 3, 7, 15, 31, 63;
%e A228035 1, 1, 7, 1,  31, 21, 127;
%e A228035 1, 3, 1, 15, 31, 9,  127, 255;
%e A228035 1, 1, 7, 5,  1,  21, 127, 85,  511;
%e A228035 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023;
%e A228035 1, 1, 1, 1,  31, 1,  127, 17,  73,  341, 2047; etc.
%t A228035 a[n_, k_] := Denominator[(1 - 2^(n - k + 1))/(1 - 2^(k + 1))];
%t A228035 Table[a[n, k], {n, 0, 11}, {k, 0, n}] // Flatten
%o A228035 (Magma) [Denominator((1-2^(n-k+1))/(1-2^(k+1))): k in [0..n], n in [0..11]];
%Y A228035 Cf. A000225, A213243, A213245, A227984.
%K A228035 nonn,tabl,frac
%O A228035 0,3
%A A228035 _Vincenzo Librandi_, Aug 12 2013