A130711 - OEIS

%I #11 Sep 21 2024 22:56:12

%S 1,2,4,8,14,32,57,123,239,493,970,1997,3953,8017,16024,32281,64550,

%T 129742,259561,520606,1041871,2087177,4176594,8362063,16730862,

%U 33483361,66987710,134029333,268117646,536373213,1072909785,2146169660

%N Number of compositions of n such that the smallest part divides every part.

%F Inverse Moebius transform of A099036.

%F G.f.: Sum_{n>0} x^n*(1-x^n)^2/((1-2*x^n)*(1-x^n-x^(2*n))).

%e a(5)=14 because among the 16 compositions of 5 only 2+3 and 3+2 do not qualify; the others, except for the composition 5, have at least one component equal to 1.

%p G:=sum(x^n*(1-x^n)^2/((1-2*x^n)*(1-x^n-x^(2*n))), n=1..50); Gser:=series(G, x =0,40): seq(coeff(Gser,x,n),n=1..33); # _Emeric Deutsch_, Sep 08 2007

%Y Cf. A083710.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Jul 01 2007

%E More terms from _Emeric Deutsch_, Sep 08 2007