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Row sums of triangle A108556, in which row n equals the inverse binomial transform of the crystal ball sequence for D_n lattice.
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%I #6 Jun 13 2017 02:02:34

%S 1,3,9,63,433,2823,17657,107439,642529,3802167,22357097,130970271,

%T 765564049,4469342439,26073165401,152043343119,886424978881,

%U 5167271805207,30119654732489,175558462395135,1023255914549617

%N Row sums of triangle A108556, in which row n equals the inverse binomial transform of the crystal ball sequence for D_n lattice.

%C Limit a(n+1)/a(n) = 3+sqrt(8) = 5.82842712...

%F G.f.: (1-9*x+19*x^2+33*x^3-80*x^4+12*x^5)/(1-12*x+46*x^2-60*x^3+9*x^4).

%o (PARI) a(n)=local(A=vector(n+1,r,vector(n+1,c,if(r-1==0 || c-1==0,1,if(r-1==1,2*c-1, sum(j=0,c-1,binomial(r+c-j-2,c-j-1)*(binomial(2*r-2,2*j)-2*(r-1)*binomial(r-3,j-1)))))))); sum(k=0,n,polcoeff(subst(Ser(A[n+1]),x, x/(1+x))/(1+x),k))

%Y Cf. A108553, A108556.

%K nonn,easy

%O 0,2

%A _Paul D. Hanna_, Jun 10 2005