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Search: id:A005987
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| A005987 |
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Number of symmetric plane partitions of n.
(Formerly M0562)
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+0
10
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| 1, 1, 1, 2, 3, 4, 6, 8, 12, 16, 22, 29, 41, 53, 71, 93, 125, 160, 211, 270, 354, 450, 581, 735, 948, 1191, 1517, 1902, 2414, 3008, 3791, 4709, 5909, 7311, 9119, 11246, 13981, 17178, 21249, 26039, 32105, 39213, 48159, 58669, 71831, 87269
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; p. 134.
R. P. Stanley, Theory and application of plane partitions II, Studies in Appl. Math., 50 (1971), 259-279.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Corollary 7.20.5
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
R. P. Stanley, A combinatorial miscellany
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FORMULA
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G.f.: Product[ 1/(1-x^(2i-1))/(1-x^(2i))^Floor[i/2], {i, 1, Infinity} ] (R. P. Stanley)
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PROGRAM
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(PARI) a(n)=polcoeff(prod(k=1, n, (1-x^k)^-if(k%2, 1, k\4), 1+x*O(x^n)), n)
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CROSSREFS
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Cf. A000784, A000785, A000786, A000219, A048142.
Adjacent sequences: A005984 A005985 A005986 this_sequence A005988 A005989 A005990
Sequence in context: A018718 A036451 A046682 this_sequence A125895 A064428 A052810
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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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be). Additional comments from Michael Somos, May 19, 2000.
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