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%I #8 Nov 12 2019 04:17:28
%S 1,2,1,1,4,1,2,5,6,1,1,8,11,8,1,2,9,20,19,10,1,1,12,29,40,29,12,1,2,
%T 13,42,69,70,41,14,1,1,16,55,112,139,112,55,16,1,2,17,72,167,252,251,
%U 168,71,18,1,1,20,89,240,419,504,419,240,89,20,1,2,21,110,329,660,923,924
%N Triangle read by rows: T(n,k) = 2*binomial(n,k) - (1 + (-1)^(n-k))/2 (0 <= k <= n).
%C Row sums = A084174: (1, 3, 6, 14, 29, ...).
%C 2*A007318 - A128174 as infinite lower triangular matrices. - _Emeric Deutsch_, Jun 21 2007
%F G.f.: G(t,z) = (1 + z - tz - 2z^2 + 2tz^3)/((1-z^2)*(1-tz)*(1-z-tz)). - _Emeric Deutsch_, Jun 21 2007
%e First few rows of the triangle:
%e 1;
%e 2, 1;
%e 1, 4, 1;
%e 2, 5, 6, 1;
%e 1, 8, 11, 8, 1;
%e 2, 9, 20, 19, 10, 1;
%e 1, 12, 29, 40, 29, 12, 1;
%e ...
%p T := proc (n, k) options operator, arrow; 2*binomial(n, k)-1/2-(1/2)*(-1)^(n-k) end proc; for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - _Emeric Deutsch_, Jun 21 2007
%Y Cf. A128174, A084174.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Jun 14 2007
%E More terms from _Emeric Deutsch_, Jun 21 2007