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 A091714 #12 Sep 09 2024 15:00:21
%S A091714 1,3,6,10,19,31,68,120,271,567,1302,2918,7199,17071,43110,108642,
%T A091714 280935,727959,1930344,5115348,13765415,37132859,101046712,275870592,
%U A091714 758236999,2088996227,5783712268,16055661688,44729027703,124907034471
%N A091714 Row sums of triangle A052313, which is the matrix square of the triangle of circular binomial coefficients (A047996).
%C A091714 Row sums of A047996 gives the number of n-bead necklaces with 2 colors when turning over is not allowed (A000031). This sequence may be regarded as the "circular binomial transform" of A000031.
%F A091714 a(n) = sum_{k=0..n} A047996(n, k)*A000031(k).
%o A091714 (PARI) {A047996(n,k)=if(n<0 || k>n,0,if(n==0 || k==0,1, (1/n)*sumdiv(gcd(n,k),d,eulerphi(d)*binomial(n/d, k/d))))}
%o A091714 a(n)=sum(k=0,n, A047996(n,k)*sum(j=0,k, A047996(k,j)))
%Y A091714 Cf. A052313, A047996, A000031.
%K A091714 nonn
%O A091714 0,2
%A A091714 _Paul D. Hanna_, Jan 31 2004