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 A305624 #17 Sep 27 2018 08:10:17
%S A305624 0,0,0,12,120,780,4188,20400,93120,409140,1748220,7337232,30386160,
%T A305624 124696740,508250988,2061566400,8331954240,33585590580,135115594140,
%U A305624 542784981552,2178107091600,8733341736900,34996103558988,140172672276000,561255446475360,2246716252964820,8991948337723260,35983044114659472,143977928423467440,576048972752188260,2304607666801990188,9219666007300387200,36882370043723748480
%N A305624 Number of chiral pairs of rows of n colors with exactly 4 different colors.
%C A305624 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 A305624 a(n) = (k!/2) * (S2(n,k) - S2(ceiling(n/2),k)), with k=4 colors used and where S2(n,k) is the Stirling subset number A008277.
%F A305624 a(n) = (A000919(n) - A056455(n)) / 2.
%F A305624 a(n) = A000919(n) - A056311(n) = A056311(n) - A056455(n).
%F A305624 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=4 colors used.
%e A305624 For a(4) = 12, the chiral pairs are the 4! = 24 permutations of ABCD, each paired with its reverse.
%t A305624 k=4; Table[(k!/2) (StirlingS2[n,k] - StirlingS2[Ceiling[n/2],k]), {n, 1, 40}]
%o A305624 (PARI) a(n) = my(k=4); (k!/2) * (stirling(n,k,2) - stirling(ceil(n/2),k,2)); \\ _Michel Marcus_, Jun 07 2018
%Y A305624 Fourth column of A305622.
%Y A305624 A056455(n) is number of achiral rows of n colors with exactly 4 different colors.
%Y A305624 Cf. A000919, A056311.
%K A305624 nonn,easy
%O A305624 1,4
%A A305624 _Robert A. Russell_, Jun 06 2018