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%I
%S 1,2,4,9,20,45,103,238,555,1305,3090,7362,17637,42460,102670,249246,
%T 607256,1484343,3639094,8946260,22048771,54467577,134842844,334493154,
%U 831296965,2069573632,5160747114,12888640503,32234749938,80728619175,202433907465
%N Diagonal sums of number triangle A119308.
%C Hankel transform is period 12, repeat (1, 0, -1, -2, -1, 0, 1, 1, 0, 0, 0, 1).
%F a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k,j)*if(k<=j, C(j+1,2*(j-k))*A000108(j-k),0)}}.
%F G.f.: (1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5). - _Mark van Hoeij_, May 10 2013
%F Conjecture: (n+5)*(n+1)*a(n) -(2*n+5)*(n+2)*a(n-1) -(n+2)*(n+1)*a(n-2) -(n+1)*(2*n+1)*a(n-3) +(n-2)*(n+2)*a(n-4)=0. - _R. J. Mathar_, Feb 13 2015
%o (PARI) x='x+O('x^66); Vec((1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5)) \\ _Joerg Arndt_, May 11 2013
%K nonn,easy
%O 0,2
%A _Paul Barry_, Apr 01 2011
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