%I A120257
%S A120257 1,2,1,3,6,1,4,20,20,1,5,50,175,70,1,6,105,980,1764,252,1,7,196,4116,24696,
%T A120257 19404,924,1,8,336,14112,232848,731808,226512,3432,1,9,540,41580,1646568,
%U A120257 16818516,24293412,2760615,12870,1,10,825,108900,9343620,267227532,1447482465
%V A120257 1,2,-1,3,-6,-1,4,-20,-20,1,5,-50,-175,70,1,6,-105,-980,1764,252,-1,7,
               -196,-4116,24696,
%W A120257 19404,-924,-1,8,-336,-14112,232848,731808,-226512,-3432,1,9,-540,-41580,
               1646568,
%X A120257 16818516,-24293412,-2760615,12870,1,10,-825,-108900,9343620,267227532,
               -1447482465
%N A120257 Triangle of Hankel transforms of certain binomial sums.
%C A120257 Row k is the Hankel transform of sum{j=0..n, C(k+j, j)}. Absolute value 
               is reversal of A103905. Diagonal and sub-diagonals are essentially 
               signed versions of the central coefficients of certain generalized 
               Pascal-Narayana triangles (A007318, A001263, A056939, A056940, A056941).
%F A120257 T(n, k):=(cos(pi*k/2)-sin(pi*k/2))*product{j=0..n-k-1, C(2k+2+j, k+1)/
               C(k+1+j, j)}
%e A120257 Triangle begins
%e A120257 1,
%e A120257 2, -1,
%e A120257 3, -6, -1,
%e A120257 4, -20, -20, 1,
%e A120257 5, -50, -175, 70, 1,
%e A120257 6, -105, -980, 1764, 252, -1,
%e A120257 7, -196, -4116, 24696, 19404, -924, -1,
%e A120257 8, -336, -14112, 232848, 731808, -226512, -3432, 1
%Y A120257 Cf. A120258.
%Y A120257 Sequence in context: A093346 A115597 A103371 this_sequence A059298 A156914 
               A059434
%Y A120257 Adjacent sequences: A120254 A120255 A120256 this_sequence A120258 A120259 
               A120260
%K A120257 easy,sign,tabl
%O A120257 0,2
%A A120257 Paul Barry (pbarry(AT)wit.ie), Jun 13 2006