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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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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,new
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AUTHOR
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njas
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