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 A207817 a(n) = (4*n)! / (n!^4 * (n+1)). 0
 1, 12, 840, 92400, 12612600, 1955457504, 329820499008, 59064793444800, 11062343605599000, 2145275226626532000, 427760079188506384320, 87255985739923260973440, 18139177035549431752363200, 3831766983249199488516960000, 820623729024838763928509760000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of walks in 4-dimensions using steps (1,0,0,0), (0,1,0,0), (0,0,1,0) and (0,0,0,1) from (0,0,0,0) to (n,n,n,n) such that after each step we have y>=x. Number of possible necklaces consisting of n white beads, n-1 red beads, n-1 green beads, and n-1 blue beads (two necklaces are considered equivalent if they differ by a cyclic permutation). Note: the generalizations of this formula and the relation between d-dimensional walks and d-colored necklaces are also true for all d, d>=5. LINKS FORMULA G.f.: 3F2(1/4,1/2,3/4;1,2;256*x). - Benedict W. J. Irwin, Jul 13 2016 MAPLE with(combinat, multinomial): seq(multinomial(4*n, n\$4)/(n+1), n=0..20); MATHEMATICA CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {1, 2}, 256 x], {x, 0, 20}], x] (* Benedict W. J. Irwin, Jul 13 2016 *) CROSSREFS Sequence in context: A178023 A228182 A003748 * A203410 A275568 A271433 Adjacent sequences:  A207814 A207815 A207816 * A207818 A207819 A207820 KEYWORD nonn,walk AUTHOR Thotsaporn Thanatipanonda, Feb 20 2012 STATUS approved

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