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A131087 Triangle read by rows: T(n,k) = 2*binomial(n,k) - (1 + (-1)^(n-k))/2 (0 <= k <= n).

%I A131087 #8 Nov 12 2019 04:17:28
%S A131087 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 A131087 13,42,69,70,41,14,1,1,16,55,112,139,112,55,16,1,2,17,72,167,252,251,
%U A131087 168,71,18,1,1,20,89,240,419,504,419,240,89,20,1,2,21,110,329,660,923,924
%N A131087 Triangle read by rows: T(n,k) = 2*binomial(n,k) - (1 + (-1)^(n-k))/2 (0 <= k <= n).
%C A131087 Row sums = A084174: (1, 3, 6, 14, 29, ...).
%C A131087 2*A007318 - A128174 as infinite lower triangular matrices. - _Emeric Deutsch_, Jun 21 2007
%F A131087 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 A131087 First few rows of the triangle:
%e A131087   1;
%e A131087   2,  1;
%e A131087   1,  4,  1;
%e A131087   2,  5,  6,  1;
%e A131087   1,  8, 11,  8,  1;
%e A131087   2,  9, 20, 19, 10,  1;
%e A131087   1, 12, 29, 40, 29, 12,  1;
%e A131087   ...
%p A131087 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 A131087 Cf. A128174, A084174.
%K A131087 nonn,tabl
%O A131087 0,2
%A A131087 _Gary W. Adamson_, Jun 14 2007
%E A131087 More terms from _Emeric Deutsch_, Jun 21 2007