%I A005380 M1601
%S A005380 1,2,6,14,33,70,149,298,591,1132,2139,3948,7199,12894,22836,39894,
%T A005380 68982,117948,199852,335426,558429,922112,1511610,2460208,3977963,
%U A005380 6390942,10206862,16207444,25596941,40214896,62868772,97814358
%N A005380 Number of partitions of n objects of 2 colors.
%D A005380 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005380 P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 
               89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, 
               Annals of Discrete Math., 43 (1989), 89-102.
%D A005380 P. A. MacMahon, Memoir on symmetric functions of the roots of systems 
               of equations, Phil. Trans. Royal Soc. London, 181 (1890), 481-536; 
               Coll. Papers II, 32-87.
%D A005380 R. P. Stanley, Theory and application of plane partitions II, Studies 
               in Appl. Math., 50 (1971), 259-279.
%D A005380 R. P. Stanley, Conjugate trace..., J. Combin. Theory, vol. A14 53-65 
               1973, esp. p. 64.
%D A005380 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 7.99.
%H A005380 T. D. Noe, <a href="b005380.txt">Table of n, a(n) for n=0..1000</a>
%H A005380 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A005380 G.f.: Product_{k=1..infinity} 1/(1-x^k)^(k+1). EULER transform of b(n) 
               = n+1.
%p A005380 mul( (1-x^i)^(-i-1),i=1..80); series(%,x,80); seriestolist(%);
%p A005380 with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; 
               local d,j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), 
               j=1..n)/n fi end end: a:=etr (n-> n+1): seq (a(n), n=0..31); [From 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
%o A005380 (PARI) a(n)=polcoeff(prod(i=1,n,(1-x^i+x*O(x^n))^-(i+1)),n)
%Y A005380 Row sums of A060243. Cf. A000219.
%Y A005380 Sequence in context: A110524 A083404 A089351 this_sequence A124612 A124613 
               A124614
%Y A005380 Adjacent sequences: A005377 A005378 A005379 this_sequence A005381 A005382 
               A005383
%K A005380 nonn,easy,nice
%O A005380 0,2
%A A005380 N. J. A. Sloane (njas(AT)research.att.com).
%E A005380 Edited by Christian G. Bower (bowerc(AT)usa.net), Sep 07 2002