A108557 Row sums of triangle A108556, in which row n equals the inverse binomial transform of the crystal ball sequence for D_n lattice.

1, 3, 9, 63, 433, 2823, 17657, 107439, 642529, 3802167, 22357097, 130970271, 765564049, 4469342439, 26073165401, 152043343119, 886424978881, 5167271805207, 30119654732489, 175558462395135, 1023255914549617

Offset: 0

Author

Paul D. Hanna, Jun 10 2005

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A108553, A108556.

Programs

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))

Formula

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).