OFFSET
1,1
LINKS
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.
FORMULA
a(n) ~ exp(1/12) * 3^(11/12 + 12*n + 18*n^2) / (A * n^(1/12) * 2^(23/6 + 16*n + 24*n^2)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 29 2023
MATHEMATICA
G = BarnesG; a[n_] := (G[2n+1]^(2-2n) G[2n+3]^(1-2n)(G[2n+2] G[2n+4])^(2n) G[6n+3](1/3 - ((10n+2) Binomial[2n, n]^3)/((6n+3) Binomial[6n+2, 3n+1]))) /((G[4n+1] G[4n+3]^2) (Gamma[2n+1] Gamma[2n+3])^(2n)); Array[a, 6] (* Jean-François Alcover, Feb 20 2019 *)
PROG
(PARI) a(n)=(1/3-(10*n+2)/(6*n+3)*binomial(2*n, n)^3/binomial(6*n+2, 3*n+1))*prod(i=1, 2*n, prod(j=1, 2*n+2, prod(k=1, 2*n, (i+j+k-1)/(i+j+k-2))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Oct 01 2004
STATUS
approved