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 A099117 Number of rhombus tilings of a hexagon with side lengths 2n+3,2n-1,2n+3,2n+3,2n-1,2n+3 which contain the rhombus above and next to the center of the hexagon. 5
 152, 436381660, 574954797841668608, 388062759166540341977143692000, 137515819873369461005150742745259538637500000, 25797761881848486655895899589856317740988916476499759600000000 (list; graph; refs; listen; history; text; internal format)
 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. MATHEMATICA a[n_] := (1/3+2(6n^2+9n+2)/(n+1)^2 Binomial[2n, n]^3/Binomial[6n+4, 3n+2]) Product[(i+j+k-1)/(i+j+k-2), {i, 1, 2n+3}, {j, 1, 2n-1}, {k, 1, 2n+3}]; Array[a, 6] (* Jean-François Alcover, Nov 18 2018, from PARI *) PROG (PARI) a(n)=(1/3+2*(6*n*n+9*n+2)/(n+1)^2*binomial(2*n, n)^3/binomial(6*n+4, 3*n+2))*prod(i=1, 2*n+3, prod(j=1, 2*n-1, prod(k=1, 2*n+3, (i+j+k-1)/(i+j+k-2)))) CROSSREFS Cf. A099112, A099113, A099114, A099115, A099116, A008793. Sequence in context: A335091 A323319 A157881 * A109778 A156740 A095226 Adjacent sequences: A099114 A099115 A099116 * A099118 A099119 A099120 KEYWORD nonn AUTHOR Ralf Stephan, Oct 01 2004 STATUS approved

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)