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A099114
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Number of rhombus tilings of a hexagon with side lengths 2n,2n+2,2n,2n,2n+2,2n which contain the rhombus above and next to the center of the hexagon.
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5
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) ~ exp(1/12) * 3^(11/12 + 12*n + 18*n^2) / (A * n^(1/12) * 2^(23/6 + 16*n + 24*n^2)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 29 2023
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MATHEMATICA
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G = BarnesG; a[n_] := (G[2n+1]^(2-2n) G[2n+3]^(1-2n)(G[2n+2] G[2n+4])^(2n) G[6n+3](1/3 - ((10n+2) Binomial[2n, n]^3)/((6n+3) Binomial[6n+2, 3n+1]))) /((G[4n+1] G[4n+3]^2) (Gamma[2n+1] Gamma[2n+3])^(2n)); Array[a, 6] (* Jean-François Alcover, Feb 20 2019 *)
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PROG
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(PARI) a(n)=(1/3-(10*n+2)/(6*n+3)*binomial(2*n, n)^3/binomial(6*n+2, 3*n+1))*prod(i=1, 2*n, prod(j=1, 2*n+2, prod(k=1, 2*n, (i+j+k-1)/(i+j+k-2))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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