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 page 261).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..53
J. Propp, Updated article
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
FORMULA
a(n) = Product_{i=0..a-1} Product_{j=0..b-1} Product_{k=0..c-1} (i+j+k+2)/(i+j+k+1) with a=b=n, c=n+1.
a(n) = Product_{k=0..n} C(2n+k,n+k)/C(n+k,k). - Paul Barry, May 13 2008
a(n) ~ exp(1/12) * 3^(9*n^2/2 + 3*n + 5/12) / (A * n^(1/12) * 2^(6*n^2 + 4*n + 3/4)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 26 2015
MATHEMATICA
Table[Product[(i+j+k+2)/(i+j+k+1), {i, 0, n-1}, {j, 0, n-1}, {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 26 2015 *)
PROG
(PARI) a(n) = prod(k=0, n, binomial(2*n+k, n+k)/binomial(n+k, k)) \\ Michel Marcus, May 20 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 28 2002
STATUS
approved