%I #8 Aug 16 2019 14:02:29

%S 1,1,4,6,13,24,51,101,205,407,814,1624,3248,6490,12979,25950,51898,

%T 103798,207619,415288,830690,1661590,3323566,6647779,13296602,

%U 26594769,53191708,106386020,212774300,425548246,851088094,1702147791,3404222451

%N G.f.: Sum((1-x)^(2*l)*Sum(x^((2*l-1)*k)/(1-2*x+x^k)^(2*l),k=1..infinity),l=1..infinity).

%F Number of compositions of n such that the greatest part occurs with odd multiplicity.

%e a(4)=6 because we have (4),(3,1),(1,3),(2,1,1),(1,2,1) and (1,1,2).

%p G:=sum((1-x)^(2*l)*sum(x^((2*l-1)*k)/(1-2*x+x^k)^(2*l),k=1..30),l=1..20): Gser:=series(G,x=0,35): seq(coeff(Gser,x^n),n=1..33); # _Emeric Deutsch_, Jun 07 2005

%Y Cf. A105201, A105200.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Apr 12 2005

%E More terms from _Emeric Deutsch_, Jun 07 2005