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A049505
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Number of symmetric plane partitions in n-cube.
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4
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1, 2, 10, 112, 2772, 151008, 18076916, 4751252480, 2740612658576, 3468301123758080, 9627912669442441500, 58618653300361405440000, 782683432110638830001250000, 22916694891747599820616089600000, 1471328419282772010324439370939640000
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OFFSET
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0,2
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COMMENTS
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The first printing of the Bressoud book gives this formula in Eq. (6.8) as the number of totally symmetric plane partitions. For the correct formula for the number of totally symmetric plane partitions see A005157.
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REFERENCES
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D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; Eq. (6.8), p. 198.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..40
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FORMULA
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Product_{1<=i<=j<=n} (i+j+n-1)/(i+j-1).
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MAPLE
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A049505 := proc(n) local i, j; mul(mul((i+j+n-1)/(i+j-1), j=i..n), i=1..n); end;
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MATHEMATICA
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a[n_] := Product[ ((2i-2)!*(i+2n-1)!)/((i+n-1)!*(2i+n-2)!), {i, 1, n}]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jun 22 2012, after PARI *)
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PROG
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(PARI) a(n)=prod(i=1, n, prod(j=i, n, (i+j+n-1)/(i+j-1)))
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CROSSREFS
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Main diagonal of array A102539.
Main diagonal of array in A073165.
Sequence in context: A206154 A181445 A062499 * A136518 A168369 A223056
Adjacent sequences: A049502 A049503 A049504 * A049506 A049507 A049508
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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