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A005157
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Number of totally symmetric plane partitions that fit in an n x n x n box.
(Formerly M1499)
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3
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1, 2, 5, 16, 66, 352, 2431, 21760, 252586, 3803648, 74327145, 1885102080, 62062015500, 2652584509440, 147198472495020, 10606175914819584, 992340657705109416, 120567366227960791040, 19023173201224270401428, 3897937005297330777227264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also, number of 2-dimensional shifted complexes on n+1 nodes. [Klivans]
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REFERENCES
| D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; Eq. (6.8), p. 198 (corrected).
C. Klivans, Obstructions to shiftedness, Discrete Comput. Geom., 33 (2005), 535-545.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
| a(n)=product{i=1..n, product{j=i..n, product{k=j..n, (i+j+k-1)/(i+j+k-2)}}}; - Paul Barry (pbarry(AT)wit.ie), May 13 2008
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EXAMPLE
| a(2)=5 because we have: void, 1, 21/1, 22/21, and 22/22.
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MAPLE
| A005157 := proc(n) local i, j; mul(mul((i+j+n-1)/(i+2*j-2), j=i..n), i=1..n); end;
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MATHEMATICA
| Table[Product[(i+j+k-1)/(i+j+k-2), {i, n}, {j, i, n}, {k, j, n}], {n, 0, 20}] (* From Harvey P. Dale, Jul 17 2011 *)
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CROSSREFS
| Cf. A049505.
Sequence in context: A091139 A084785 A124551 * A019502 A019503 A019504
Adjacent sequences: A005154 A005155 A005156 * A005158 A005159 A005160
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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