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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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D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; p. 134.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
Sequence in context: A018718 A036451 A046682 this_sequence A125895 A064428 A052810
Adjacent sequences: A005984 A005985 A005986 this_sequence A005988 A005989 A005990
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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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