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%I A338956 #17 Dec 20 2020 02:21:43
%S A338956 1,137548893254081168086800766,
%T A338956 11046328890861010626464488614428032600986342,
%U A338956 10897746068335468788318134977474134922662053604436974448,21912802868317153141871319582922663027477920477404414535105616050
%N A338956 Number of oriented colorings of the 96 edges (or triangular faces) of the 4-D 24-cell using exactly n colors.
%C A338956 Each chiral pair is counted as two when enumerating oriented arrangements. The Schläfli symbol of the 24-cell is {3,4,3}. It has 24 octahedral facets. It is self-dual. For n>96, a(n) = 0.
%H A338956 Robert A. Russell, <a href="/A338956/b338956.txt">Table of n, a(n) for n = 1..96</a>
%F A338956 A338952(n) = Sum_{j=1..Min(n,96)} a(n) * binomial(n,j).
%F A338956 a(n) = A338957(n) + A338958(n) = 2*A338957(n) - A338959(n) = 2*A338958(n) + A338959(n).
%t A338956 bp[j_] := Sum[k! StirlingS2[j, k] x^k, {k, 0, j}] (* binomial series *)
%t A338956 Drop[CoefficientList[bp[8]/6+bp[12]/4+bp[16]/12+bp[18]/18+7bp[24]/48+bp[32]/12+bp[36]/18+19bp[48]/576+bp[50]/8+bp[96]/576,x],1]
%Y A338956 Cf. A338957 (unoriented), A338958 (chiral), A338959 (achiral), A338952 (up to n colors), A338948 (vertices, facets), A331350 (5-cell), A331358 (8-cell edges, 16-cell faces), A331354 (16-cell edges, 8-cell faces), A338980 (120-cell, 600-cell).
%K A338956 nonn
%O A338956 1,2
%A A338956 _Robert A. Russell_, Nov 17 2020

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