A108555 Antidiagonal sums of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.

1, 2, 5, 12, 35, 116, 411, 1482, 5333, 19030, 67265, 235704, 819863, 2834600, 9752951, 33428054, 114228713, 389419114, 1325155261, 4503031332, 15285291851, 51842203804, 175719341971, 595316455842, 2016131645245, 6826076021310

Offset: 0

Author

Paul D. Hanna, Jun 10 2005

Keywords

• nonn

Comments

Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3).

Crossrefs

Cf. A108553, A108554.

Programs

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)))))))}

Formula

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]