%I A052839
%S A052839 1,2,2,3,3,4,5,6,7,9,11,13,16,19,23,28,33,39,47,55,65,77,90,105,123,
%T A052839 143,166,193,223,257,297,341,391,449,513,586,669,761,865,983,1114,1261,
%U A052839 1427,1611,1817,2049,2305,2591,2911,3265,3659,4098,4583,5121,5719,6379
%N A052839 Number of partitions of n into distinct summands (A000009), plus 1 (apart 
               from the first term).
%H A052839 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=806">
               Encyclopedia of Combinatorial Structures 806</a>
%F A052839 G.f.: (-x-exp(Sum(-(-1)^(j[1]+1)*x^j[1]/(x^j[1]-1)/j[1], j[1]=1 .. infinity))+exp(Sum(-(-1)^(j[1]+1)*x^j[1]/
               (x^j[1]-1)/j[1], j[1]=1 .. infinity))*x)/(-1+x)
%p A052839 spec := [S,{C=Sequence(Z,1 <= card),B=PowerSet(C),S=Union(B,C)},unlabeled]: 
               seq(combstruct[count](spec,size=n), n=0..67);
%p A052839 Or: with(gfun,seriestolist); seriestolist(series(mul(1+z^i,i=1..81)+z/
               (1-z),z,81));
%Y A052839 Apart from the first term equals A000009 + 1 and also the left edge of 
               A068049.
%Y A052839 Sequence in context: A026798 A125890 A067661 this_sequence A125894 A091493 
               A058724
%Y A052839 Adjacent sequences: A052836 A052837 A052838 this_sequence A052840 A052841 
               A052842
%K A052839 easy,nonn
%O A052839 0,2
%A A052839 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052839 Edited by Antti Karttunen, Feb 13 2002, based on information received 
               from Bruno Salvy.