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Search: id:A000990
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| A000990 |
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Number of plane partitions of n with at most two rows.
(Formerly M2462 N0978)
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+0
8
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| 1, 1, 3, 5, 10, 16, 29, 45, 75, 115, 181, 271, 413, 605, 895, 1291, 1866, 2648, 3760, 5260, 7352, 10160, 14008, 19140, 26085, 35277, 47575, 63753, 85175, 113175, 149938, 197686, 259891, 340225, 444135, 577593, 749131, 968281, 1248320
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals row sums of triangle A147767 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 11 2008]
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 105.
L. Carlitz, Generating functions and partition problems, pp. 144-169 of A. L. Whiteman, ed., Theory of Numbers, Proc. Sympos. Pure Math., 8 (1965). Amer. Math. Soc., see p. 145, eq. (1.7).
M. S. Cheema and B. Gordon, Some remarks on two- and three-line partitions, Duke Math. J., 31 (1964), 267-273.
P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116.
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FORMULA
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G.f.: Product ( 1 - x^m )^(-2) (m=2..inf) / ( 1 - x ).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff((1-x)/prod(k=1, n, 1-x^k, 1+x*O(x^n))^2, n)) /* Michael Somos Jan 29 2005 */
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CROSSREFS
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Antidiagonal sums of triangle A093010.
A147767 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 11 2008]
Sequence in context: A032279 A070558 A070559 this_sequence A129361 A062773 A079934
Adjacent sequences: A000987 A000988 A000989 this_sequence A000991 A000992 A000993
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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