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 A056346 #29 Oct 13 2018 09:29:57
%S A056346 0,0,0,0,0,60,1080,11970,105840,821952,5874480,39713550,258136200,
%T A056346 1631273220,10096734312,61536377700,370710950400,2213749658880,
%U A056346 13132080672480,77509456944318,455754569692680
%N A056346 Number of bracelets of length n using exactly six different colored beads.
%C A056346 Turning over will not create a new bracelet.
%D A056346 M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%F A056346 a(n) = A056341(n) - 6*A032276(n) + 15*A032275(n) - 20*A027671(n) + 15*A000029(n) - 6.
%F A056346 From _Robert A. Russell_, Sep 27 2018: (Start)
%F A056346 a(n) = (k!/4) * (S2(floor((n+1)/2),k) + S2(ceiling((n+1)/2),k)) + (k!/2n) * Sum_{d|n} phi(d) * S2(n/d,k), where k=6 is the number of colors and S2 is the Stirling subset number A008277.
%F A056346 G.f.: (k!/4) * x^(2k-2) * (1+x)^2 / Product_{i=1..k} (1-i x^2) - Sum_{d>0} (phi(d)/2d) * Sum_{j} (-1)^(k-j) * C(k,j) * log(1-j x^d), where k=6 is the number of colors. (End)
%e A056346 For a(6)=60, pair up the 120 permutations of BCDEF, each with its reverse, such as BCDEF-FEDCB. Precede the first of each pair with an A, such as ABCDEF. These are the 60 arrangements, all chiral. If we precede the second of each pair with an A, such as AFEDCB, we get the chiral partner of each. - _Robert A. Russell_, Sep 27 2018
%t A056346 t[n_, k_] := (For[t1 = 0; d = 1, d <= n, d++, If[Mod[n, d] == 0, t1 = t1 + EulerPhi[d]*k^(n/d)]]; If[EvenQ[n], (t1 + (n/2)*(1 + k)*k^(n/2))/(2*n), (t1 + n*k^((n + 1)/2))/(2*n)]);
%t A056346 T[n_, k_] := Sum[(-1)^i*Binomial[k, i]*t[n, k - i], {i, 0, k - 1}];
%t A056346 a[n_] := T[n, 6];
%t A056346 Array[a, 21] (* _Jean-François Alcover_, Nov 05 2017, after _Andrew Howroyd_ *)
%t A056346 k=6; Table[k! DivisorSum[n, EulerPhi[#] StirlingS2[n/#,k]&]/(2n) + k!(StirlingS2[Floor[(n+1)/2], k] + StirlingS2[Ceiling[(n+1)/2], k])/4, {n,1,30}] (* _Robert A. Russell_, Sep 27 2018 *)
%o A056346 (PARI) a(n) = my(k=6); (k!/4) * (stirling(floor((n+1)/2),k,2) + stirling(ceil((n+1)/2),k,2)) + (k!/(2*n))*sumdiv(n, d, eulerphi(d)*stirling(n/d,k,2)); \\ _Michel Marcus_, Sep 29 2018
%Y A056346 Column 6 of A273891.
%Y A056346 Equals (A056286 + A056492) / 2 = A056286 - A305545 = A305545 + A056492.
%Y A056346 Cf. A008277.
%K A056346 nonn
%O A056346 1,6
%A A056346 _Marks R. Nester_