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 A305626 #16 Sep 27 2018 08:10:07
%S A305626 0,0,0,0,0,360,7560,95760,952560,8217720,64614960,476514360,
%T A305626 3355664760,22837086720,151449482520,984573465120,6302069010720,
%U A305626 39847409421480,249509368422720,1550188394120520,9570844541994120,58789922099665680,359629148397511080,2192484972513916080,13329510116645202480,80854267307329446840,489528474458978944080,2959252601445086408280,17866194139995100525080,107751636988750077294240,649286502010403671101240
%N A305626 Number of chiral pairs of rows of n colors with exactly 6 different colors.
%C A305626 If the row is achiral, i.e., the same as its reverse, we ignore it. If different from its reverse, we count it and its reverse as a chiral pair.
%F A305626 a(n) = (k!/2) * (S2(n,k) - S2(ceiling(n/2),k)), with k=6 colors used and where S2(n,k) is the Stirling subset number A008277.
%F A305626 a(n) = (A000920(n) - A056457(n)) / 2.
%F A305626 a(n) = A000920(n) - A056313(n) = A056313(n) - A056457(n).
%F A305626 G.f.: -(k!/2) * (x^(2k-1) + x^(2k)) / Product_{j=1..k} (1 - j*x^2) + (k!/2) * x^k / Product_{j=1..k} (1 - j*x) with k=6 colors used.
%e A305626 For a(6) = 360, the chiral pairs are the 6! = 720 permutations of ABCDEF, each paired with its reverse.
%t A305626 k=6; Table[(k!/2) (StirlingS2[n,k] - StirlingS2[Ceiling[n/2],k]), {n, 1, 40}]
%o A305626 (PARI) a(n) = 360*(stirling(n, 6, 2) - stirling(ceil(n/2), 6, 2)); \\ _Altug Alkan_, Sep 26 2018
%Y A305626 Sixth column of A305622.
%Y A305626 A056457(n) is number of achiral rows of n colors with exactly 6 different colors.
%Y A305626 Cf. A000920, A056313.
%K A305626 nonn,easy
%O A305626 1,6
%A A305626 _Robert A. Russell_, Jun 06 2018