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A005987 Number of symmetric plane partitions of n.
(Formerly M0562)
11
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; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

R. P. Stanley, A combinatorial miscellany

FORMULA

G.f.: Product[ 1/(1-x^(2i-1))/(1-x^(2i))^Floor[i/2], {i, 1, Infinity} ] (R. P. Stanley).

MATHEMATICA

terms = 46; s = Product[1/(1 - x^(2i-1))/(1 - x^(2i))^Floor[i/2], {i, 1, Ceiling[terms/2]}] + O[x]^terms; CoefficientList[s, x] (* Jean-Fran├žois Alcover, Jul 10 2017 *)

PROG

(PARI) a(n)=polcoeff(prod(k=1, n, (1-x^k)^-if(k%2, 1, k\4), 1+x*O(x^n)), n)

CROSSREFS

Cf. A000784, A000785, A000786, A000219, A048142.

Sequence in context: A241743 A180652 A046682 * A241828 A125895 A241344

Adjacent sequences:  A005984 A005985 A005986 * A005988 A005989 A005990

KEYWORD

nonn,nice,easy,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wouter Meeussen, Dec 11 1999

Additional comments from Michael Somos, May 19 2000

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.