Search: id:A000990
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%I A000990 M2462 N0978
%S A000990 1,1,3,5,10,16,29,45,75,115,181,271,413,605,895,1291,1866,2648,3760,
%T A000990 5260,7352,10160,14008,19140,26085,35277,47575,63753,85175,113175,
%U A000990 149938,197686,259891,340225,444135,577593,749131,968281,1248320
%N A000990 Number of plane partitions of n with at most two rows.
%C A000990 Equals row sums of triangle A147767 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Nov 11 2008]
%D A000990 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000990 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000990 G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 
               2004. page 105.
%D A000990 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).
%D A000990 M. S. Cheema and B. Gordon, Some remarks on two- and three-line partitions, 
               Duke Math. J., 31 (1964), 267-273.
%D A000990 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.
%F A000990 G.f.: Product ( 1 - x^m )^(-2) (m=2..inf) / ( 1 - x ).
%o A000990 (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 */
%Y A000990 Antidiagonal sums of triangle A093010.
%Y A000990 A147767 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 11 2008]
%Y A000990 Sequence in context: A032279 A070558 A070559 this_sequence A129361 A062773 
               A079934
%Y A000990 Adjacent sequences: A000987 A000988 A000989 this_sequence A000991 A000992 
               A000993
%K A000990 nonn,easy
%O A000990 0,3
%A A000990 N. J. A. Sloane (njas(AT)research.att.com).

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