

A099114


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.


5




OFFSET

1,1


LINKS

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.


MATHEMATICA

G = BarnesG; a[n_] := (G[2n+1]^(22n) G[2n+3]^(12n)(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] (* JeanFrançois Alcover, Feb 20 2019 *)


PROG

(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+k1)/(i+j+k2))))


CROSSREFS

Cf. A099112, A099113, A099115, A099116, A099117, A008793.
Sequence in context: A172824 A070632 A234039 * A013810 A172875 A172839
Adjacent sequences: A099111 A099112 A099113 * A099115 A099116 A099117


KEYWORD

nonn


AUTHOR

Ralf Stephan, Oct 01 2004


STATUS

approved



