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
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
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=n, b=n+1, c=n+2.
a(n) = (-1)^floor((n+1)/2)*det(M(n+1)) where M(n) is the n X n matrix m(i, j)=C(2n, i+j), with i and j ranging from 1 to n. - Benoit Cloitre, Jan 31 2003
a(n) = (1/2)*Product[Product[Product[(i+j+k-1)/(i+j+k-2),{i,1,n+1}],{j,1,n+1}],{k,1,n+1}]. a(n) = A008793(n+1)/2. - Alexander Adamchuk, Jul 10 2006
a(n) ~ exp(1/12) * 3^(9*n^2/2 + 9*n + 53/12) / (A * n^(1/12) * 2^(6*n^2 + 12*n + 27/4)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 26 2015
MATHEMATICA
Table[Product[Product[Product[(i+j+k-1)/(i+j+k-2), {i, 1, n+1}], {j, 1, n+1}], {k, 1, n+1}], {n, 0, 10}]/2 (* Alexander Adamchuk, Jul 10 2006 *)
PROG
(PARI) {a(n) = abs(matdet(matrix(n+1, n+1, i, j, binomial(2*(n+1), i+j))))}; \\ Shifted by Georg Fischer, Jun 19 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 28 2002
STATUS
approved