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A099113
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Number of rhombus tilings of a hexagon with all sides of length 2n+1 which contain the rhombus above and next to the center of the hexagon.
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5
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364, 94682016, 13704096621766720, 1074416738842280125146121600, 45276656003305722314718295417920118125000, 1022271041965503132822786100650613600920143229195000000000
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..6.
M. Fulmek and C. Krattenthaler, The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II, arXiv:math/9909038 [math.CO], 1999.
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MATHEMATICA
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G = BarnesG; a[n_] := (G[2n+2]^(1-4n) G[2n+3]^(4n+2) G[6n+4] (Binomial[2n, n]^3/Binomial[6n+2, 3n+1]+1) Gamma[2n+2]^(-4n-2))/(3G[4n+3]^3); Array[a, 6] (* Jean-François Alcover, Feb 20 2019 *)
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PROG
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(PARI) a(n)=(1/3+1/3*binomial(2*n, n)^3/binomial(6*n+2, 3*n+1))*prod(i=1, 2*n+1, prod(j=1, 2*n+1, prod(k=1, 2*n+1, (i+j+k-1)/(i+j+k-2))))
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CROSSREFS
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Cf. A099112, A099114, A099115, A099116, A099117, A008793.
Sequence in context: A022196 A098252 A221393 * A350555 A073304 A011763
Adjacent sequences: A099110 A099111 A099112 * A099114 A099115 A099116
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Oct 01 2004
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STATUS
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approved
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