|
%I #26 Feb 07 2018 09:41:05
%S 1,2,-1,2,1,-1,2,3,0,-1,2,5,3,-1,-1,2,7,8,2,-2,-1,2,9,15,10,0,-3,-1,2,
%T 11,24,25,10,-3,-4,-1,2,13,35,49,35,7,-7,-5,-1,2,15,48,84,84,42,0,-12,
%U -6,-1,2,17,63,132,168,126,42,-12,-18,-7,-1,2,19,80,195,300,294,168,30,-30,-25,-8,-1
%N Triangle read by rows; row 0 is 1; the n-th row for n>0 contains the coefficients in the expansion of (2-x)*(1+x)^(n-1).
%H Seiichi Manyama, <a href="/A298485/b298485.txt">Rows n = 0..139, flattened</a>
%F T(n,k) = T(n-1,k-1)+T(n-1,k); T(0,0)=1, T(1,0)=2, T(1,1)=-1.
%e Triangle begins:
%e 1;
%e 2, -1;
%e 2, 1, -1;
%e 2, 3, 0, -1;
%e 2, 5, 3, -1, -1;
%e 2, 7, 8, 2, -2, -1;
%e 2, 9, 15, 10, 0, -3, -1;
%e 2, 11, 24, 25, 10, -3, -4, -1;
%e 2, 13, 35, 49, 35, 7, -7, -5, -1;
%e ...
%t T[0, 0] = 1; T[_, 0] = 2; T[1, 1] = -1; T[n_?Positive, k_?Positive] := T[n, k] = T[n - 1, k - 1] + T[n - 1, k]; T[_, _] = 0; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 05 2018 *)
%Y Central column gives A088218.
%Y Cf. A037012.
%K sign,tabl
%O 0,2
%A _Seiichi Manyama_, Jan 20 2018
|
