

A099112


Number of rhombus tilings of a hexagon with all sides of length 2n which contain the rhombus above and next to the center of the hexagon.


5



6, 73080, 472598638512, 1631619756904447290240, 3008692066440440678503082183460000, 2962701176869736970134706082584757742017500000000, 1557551298812773746701490125169378658941648550102913633903040000000
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..7.
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

a[n_] := (1/3  1/12 Binomial[2n, n]^3/Binomial[6n, 3n]) Product[(i + j + k  1)/(i + j + k  2), {i, 1, 2n}, {j, 1, 2n}, {k, 1, 2n}];
Array[a, 6] (* JeanFrançois Alcover, Nov 18 2018 *)


PROG

(PARI) a(n)=(1/31/12*binomial(2*n, n)^3/binomial(6*n, 3*n))*prod(i=1, 2*n, prod(j=1, 2*n, prod(k=1, 2*n, (i+j+k1)/(i+j+k2))))


CROSSREFS

Cf. A099113, A099114, A099115, A099116, A099117, A008793.
Sequence in context: A076913 A101450 A101439 * A172750 A086897 A034208
Adjacent sequences: A099109 A099110 A099111 * A099113 A099114 A099115


KEYWORD

nonn


AUTHOR

Ralf Stephan, Oct 01 2004


STATUS

approved



