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%I #24 Oct 29 2021 06:20:49
%S 1,2,1,3,1,1,4,1,3,1,5,1,5,4,1,6,1,7,4,7,1,8,1,11,4,19,16,18,1,9,1,13,
%T 4,25,16,38,29,1,10,1,15,4,31,16,58,57,47,1,11,1,17,4,37,16,78,64,117,
%U 76,1,12,1,19,4,43,16,98,64,187,193,123,1
%N Rectangular array read by antidiagonals, with entry k in row n given by T(n,k) = 2^{k-1}*Sum_{j=1..n} (cos((2*j-1)*Pi/(2*n+1)))^{k-1}.
%C Antidiagonal sums: {1,3,5,9,16,26,46,78,136,...}.
%F T(n,k) = 2^{k-1}*Sum_{j=1..n} (cos((2*j-1)*Pi/(2*n+1)))^{k-1}.
%F Empirical g.f. for row n: F(x) = (Sum_{u=0..n-1} A122765(n,n-1-u)*x^u)/(Sum_{v=0..n} A108299(n,v)*x^v).
%F Empirical: odd column first differences tend to A000984 = {1, 2, 6, 20, 70, 252, ...} (central binomial coefficients).
%e Array begins as
%e .1..1...1..1...1...1
%e .2..1...3..4...7..11
%e .3..1...5..4..13..16
%e .4..1...7..4..19..16
%e .5..1...9..4..25..16
%e .6..1..11..4..31..16
%Y Rows: cf. A000012, A000032, A094649, A189234, A216605, etc.
%Y Cf. A185095, A186740.
%K nonn,tabl
%O 1,2
%A _L. Edson Jeffery_, Jan 12 2013
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