

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
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OFFSET

0,2


COMMENTS

Number of walks in 4dimensions 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, n1 red beads, n1 green beads, and n1 blue beads (two necklaces are considered equivalent if they differ by a cyclic permutation).
Note: the generalizations of this formula and the relation between ddimensional walks and dcolored necklaces are also true for all d, d>=5.


LINKS

Table of n, a(n) for n=0..14.


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: A228182 A003748 A280333 * A203410 A275568 A271433
Adjacent sequences: A207814 A207815 A207816 * A207818 A207819 A207820


KEYWORD

nonn,walk


AUTHOR

Thotsaporn Thanatipanonda, Feb 20 2012


STATUS

approved



