%I A102712
%S A102712 1,3,8,19,43,94,202,428,899,1875,3890,8036,16544,33962,69552,142149,
%T A102712 290017,590814,1202016,2442706,4958974,10058216,20384498,41282346,
%U A102712 83549603,168992081,341627732,690279026,1394115072,2814430326
%N A102712 Sum of largest parts of all compositions of n.
%F A102712 G.f.: Sum(n*(1-x)^2*x^n/((1-2*x+x^n)*(1-2*x+x^(n+1))), n=1..infinity).
%F A102712 G.f.: (1-x)/(1-2*x)*Sum(x^n/(1-2*x+x^n),n=1..infinity). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Apr 28 2008
%e A102712 a(4)=19 because we have (4), (3)1, 1(3), (2)2, (2)11, 1(2)1, 11(2) and 
               (1)111; the largest parts, shown between parentheses, add up to 19.
%p A102712 G:=sum(n*(1-x)^2*x^n/((1-2*x+x^n)*(1-2*x+x^(n+1))),n=1..45):Gser:=series(G,
               x=0,40):seq(coeff(Gser,x^n),n=1..36); (Deutsch)
%Y A102712 Cf. A006128, A097939.
%Y A102712 Sequence in context: A065352 A161993 A008466 this_sequence A054480 A121551 
               A077850
%Y A102712 Adjacent sequences: A102709 A102710 A102711 this_sequence A102713 A102714 
               A102715
%K A102712 easy,nonn
%O A102712 1,2
%A A102712 Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2005
%E A102712 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2005