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 A108999 #13 Aug 31 2025 05:29:35
%S A108999 1,2,16,170,1856,20082,214864,2282394,24165120,255708578,2708805776,
%T A108999 28752157898,305908697152,3262741154194,34882914424528,
%U A108999 373781033269306,4013444615232512,43174945822078530,465247083731404048
%N A108999 Main diagonal of square array A108998, in which row n equals the coordination sequence of B_n lattice.
%C A108999 Compare to diagonal A108554 of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.
%H A108999 Muniru A Asiru, <a href="/A108999/b108999.txt">Table of n, a(n) for n = 0..900</a>
%F A108999 a(n) = Sum_{j=0..n} C(2*n-j-1, n-j)*( C(2*n+1, 2*j) - 2*n*C(n-1, j-1) ).
%F A108999 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 A108999 a[n_]:= Sum[Binomial[2*n-j-1, n-j]*(Binomial[2*n+1, 2*j] - 2*n*Binomial[n-1, j-1]), {j,0,n}]; Array[a, 20, 0] (* _Stefano Spezia_, Nov 21 2018 *)
%o A108999 (PARI) {a(n)=sum(j=0,n, binomial(2*n-j-1,n-j)*(binomial(2*n+1,2*j)-2*n*binomial(n-1,j-1)))}
%o A108999 (GAP) List([0..20],n->Sum([0..n],j->Binomial(2*n-j-1,n-j)*(Binomial(2*n+1,2*j)-2*n*Binomial(n-1,j-1)))); # _Muniru A Asiru_, Nov 21 2018
%Y A108999 Cf. A108998, A109000, A109001.
%K A108999 nonn,changed
%O A108999 0,2
%A A108999 _Paul D. Hanna_, Jun 17 2005