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.
Theresia Eisenkölbl, Rhombus Tilings of a Hexagon with Three Fixed Border Tiles, 1998.
J. Propp, Update on Enumeration of Matchings, 2009.
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
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