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%I #21 Feb 28 2019 03:15:57
%S 0,0,720,0,0,3600,2400,4320,28800,35400,64800,284400,540000,1139400,
%T 3708000,8557200,19677600,55725120,140359200,346456800,935942400,
%U 2442469200,6282571680
%N Number of n-cycles on the graph of the regular 120-cell, 3 <= n <= 600.
%C The 120-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol of the 120-cell is {5,3,3}.
%H A. Weimholt, <a href="http://www.weimholt.com/andrew/120.html">120-cell net</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/120-Cell.html">120-Cell</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclePolynomial.html">Cycle Polynomial</a>
%e a(5) = 720, because there are 720 5-cycles on the graph of the 120-cell.
%e Cycle polynomial is 720*x^5 + 3600*x^8 + 2400*x^9 + 4320*x^10 + 28800*x^11 + 35400*x^12 + 64800*x^13 + 284400*x^14 + 540000*x^15 + 1139400*x^16 + 3708000*x^17 + 8557200*x^18 + 19677600*x^19 + 55725120*x^20 + 140359200*x^21 + 346456800*x^22 + 935942400*x^23 + ...
%Y Cf. A167981 (2n-cycles on graph of the tesseract).
%Y Cf. A167982 (n-cycles on graph of 16-cell).
%Y Cf. A167983 (n-cycles on graph of 24-cell).
%Y Cf. A167985 (n-cycles on graph of 600-cell).
%Y Cf. A085452 (2k-cycles on graph of n-cube).
%Y Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
%Y Cf. A167986 (k-cycles on graph of n-orthoplex).
%Y Cf. A108997 (number of vertices n-steps from a given vertex on graph of 120-cell).
%K fini,more,nonn,hard
%O 3,3
%A _Andrew Weimholt_, Nov 16 2009
%E a(24) from _Eric W. Weisstein_, Feb 21 2014
%E a(25) from _Eric W. Weisstein_, Mar 11 2014
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