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%I #6 Nov 21 2012 08:54:05
%S 1,2,5,12,35,116,411,1482,5333,19030,67265,235704,819863,2834600,
%T 9752951,33428054,114228713,389419114,1325155261,4503031332,
%U 15285291851,51842203804,175719341971,595316455842,2016131645245,6826076021310
%N Antidiagonal sums of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.
%C Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3).
%F Empirical G.f.: (x^3+x^2+x-1)*(2*x^5+5*x^4-4*x^3+10*x^2-6*x+1) / ((x-1)^2*(x^2+2*x-1)^2*(x^3+x^2+3*x-1)). [_Colin Barker_, Nov 21 2012]
%o (PARI) {a(n)=if(n<0,0,if(n==0,1,sum(k=0,n,sum(j=0,k,binomial(n-j,k-j)* (binomial(2*(n-k),2*j)-2*j*(n-k-j)*binomial(n-k,j)/if(n==k+1,1,(n-k-1)))))))}
%Y Cf. A108553, A108554.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 10 2005
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