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 A372145 #36 Jun 29 2024 03:34:36
%S A372145 1,2,4,12,48,288,2304,26880,430080,10035200,321126400,14836039680,
%T A372145 949506539520,87734404251648,11230003744210944,2064716402685640704,
%U A372145 528567399087524020224,194361783607326689722368,99513233206951265137852416,72958995691997968023051829248,74710011588605919255605073149952
%N A372145 Number of domino tilings of the order n Aztec diamond which are centrally symmetric.
%H A372145 Bo-Yin Yang, <a href="https://dspace.mit.edu/handle/1721.1/13937">Two Enumeration Problems about the Aztec Diamonds</a>, MIT, 1991.
%F A372145 Let H_j(n) = Product_{1<=k<n/j} (n-j*k)!.
%F A372145 For n>=1, we have [see Bo-Yin Yang, Thm. 4.1]:
%F A372145 a(2*n) = 2^n * a(2*n-1);
%F A372145 a(4*n-1) = 2^(2*n^2-2*n+1)*H(4,4*n+3)*H(4,4*n-1)*(H(1,n)*H(1,n-1))^2/(H(2,2*n-1)*H(2,2*n+1))^3;
%F A372145 a(4*n+1) = 2^(2*n^2+1)*H(4,4*n+3)^2*H(1,n)^4/H(2,2*n+1)^6.
%Y A372145 Cf. A006125, A005158.
%K A372145 nonn
%O A372145 0,2
%A A372145 _Ludovic Schwob_, Jun 27 2024