This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108554 #8 Aug 31 2025 07:50:16
%S A108554 1,3,13,147,1681,18733,204205,2195399,23429185,249258777,2650436845,
%T A108554 28209301211,300745906449,3212758605189,34392151363021,
%U A108554 368908132170511,3964622452867329,42682164804034609,460242445806795853
%N A108554 Main diagonal of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.
%C A108554 Limit a(n+1)/a(n) ~ 11.08...
%C A108554 Limit is equal to A001622^5 = A244593 = 11.090169943749474241... - _Vaclav Kotesovec_, Aug 31 2025
%F A108554 a(n) ~ phi^(5*n + 1) / (2*5^(1/4)*sqrt(Pi*n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Aug 31 2025
%t A108554 Join[{1, 3}, Table[Sum[Binomial[2*n - j, n - j]*(Binomial[2*n, 2*j] - 2*j*(n - j)*Binomial[n, j]/(n - 1)), {j, 0, n}], {n, 2, 20}]] (* _Vaclav Kotesovec_, Aug 31 2025 *)
%o A108554 (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 A108554 Cf. A108553, A108555, A244593.
%K A108554 nonn,changed
%O A108554 0,2
%A A108554 _Paul D. Hanna_, Jun 10 2005