A108554 - OEIS

%I #3 Mar 30 2012 18:36:46

%S 1,3,13,147,1681,18733,204205,2195399,23429185,249258777,2650436845,

%T 28209301211,300745906449,3212758605189,34392151363021,

%U 368908132170511,3964622452867329,42682164804034609,460242445806795853

%N Main diagonal of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.

%C Limit a(n+1)/a(n) ~ 11.08...

%o (PARI) {a(n)=if(n<0,0,if(n==0,1,if(n==1,3,sum(j=0,n,binomial(2*n-j,n-j)* (binomial(2*n,2*j)-2*j*(n-j)*binomial(n,j)/(n-1))))))}

%Y Cf. A108553, A108555.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 10 2005