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A071091
Number of tilings by lozenges of hexagon with sides 2n, 2n+3, 2n, 2n+3, 2n, 2n+3 and middle triangle in each edge removed.
0
1, 6272, 23763455716, 55031753041200000000, 73940670068249096897010952625900, 56037490591783745726843246231095021363200000000, 23568709541875843004154233224481427781479176313098933529600000000
OFFSET
0,2
REFERENCES
J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 2).
LINKS
M. Ciucu et al., Enumeration of lozenge tilings of hexagons with a central triangular hole, arXiv:math/9912053 [math.CO], 1999.
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
FORMULA
a(n) = (n+1)^3 * (3*n+1) * (3*n+2)^2 * pochhammer(n+2, 2*n)^6 * S(2*n)^3 * S(6*n+2) / S(4*n+2)^3 where S(n) = A000178(n) = Product_{k=0..n} k! [Corollary 2 of Eisenkölbl]. - Sean A. Irvine, Jun 27 2024
CROSSREFS
Sequence in context: A234440 A254635 A189655 * A209826 A107582 A213869
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 28 2002
EXTENSIONS
Offset corrected and more terms from Sean A. Irvine, Jun 27 2024
STATUS
approved