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A099112 Number of rhombus tilings of a hexagon with all sides of length 2n which contain the rhombus above and next to the center of the hexagon. 5
6, 73080, 472598638512, 1631619756904447290240, 3008692066440440678503082183460000, 2962701176869736970134706082584757742017500000000, 1557551298812773746701490125169378658941648550102913633903040000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) ~ exp(1/12) * 3^(18*n^2 - 13/12) / (A * n^(1/12) * 2^(24*n^2 - 1/6)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 29 2023
MATHEMATICA
a[n_] := (1/3 - 1/12 Binomial[2n, n]^3/Binomial[6n, 3n]) Product[(i + j + k - 1)/(i + j + k - 2), {i, 1, 2n}, {j, 1, 2n}, {k, 1, 2n}];
Array[a, 6] (* Jean-François Alcover, Nov 18 2018 *)
PROG
(PARI) a(n)=(1/3-1/12*binomial(2*n, n)^3/binomial(6*n, 3*n))*prod(i=1, 2*n, prod(j=1, 2*n, prod(k=1, 2*n, (i+j+k-1)/(i+j+k-2))))
CROSSREFS
Sequence in context: A076913 A101450 A101439 * A172750 A086897 A034208
KEYWORD
nonn
AUTHOR
Ralf Stephan, Oct 01 2004
STATUS
approved

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Last modified April 24 18:17 EDT 2024. Contains 371962 sequences. (Running on oeis4.)