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 A331352 #14 Mar 09 2024 12:06:12
%S A331352 0,6,405,7904,76880,486522,2300305,8806336,28725192,82626270,
%T A331352 214744629,513368064,1144198952,2402617490,4792612545,9142333696,
%U A331352 16768783408,29707141878,51023629173,85234690080,138859666848
%N A331352 Number of chiral pairs of colorings of the edges (or triangular faces) of a regular 4-dimensional simplex with n available colors.
%C A331352 A 4-dimensional simplex has 5 vertices and 10 edges. Its Schläfli symbol is {3,3,3}. The chiral colorings of its edges come in pairs, each the reflection of the other.
%H A331352 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
%F A331352 a(n) = (24*n^2 - 50*n^3 + 20*n^4 + 15*n^6 - 10*n^7 + n^10) / 120.
%F A331352 a(n) = 6*C(n,2) + 387*C(n,3) + 6320*C(n,4) + 41350*C(n,5) + 135792*C(n,6) + 246540*C(n,7) + 252000*C(n,8) + 136080*C(n,9) + 30240*C(n,10), where the coefficient of C(n,k) is the number of colorings using exactly k colors.
%F A331352 a(n) = A331350(n) - A063843(n) = (A331350(n) - A331353(n)) / 2 = A063843(n) - A331353(n).
%t A331352 Table[(24n^2 - 50n^3 + 20n^4 + 15n^6 - 10n^7 + n^10)/120, {n, 1, 25}]
%Y A331352 Cf. A331350 (oriented), A063843 (unoriented), A331353 (achiral).
%Y A331352 Other polychora: A331360 (8-cell), A331356 (16-cell), A338954 (24-cell), A338966 (120-cell, 600-cell).
%Y A331352 Row 4 of A327085 (simplex edges and ridges) and A337885 (simplex faces and peaks).
%K A331352 nonn,easy
%O A331352 1,2
%A A331352 _Robert A. Russell_, Jan 14 2020