A130711 Number of compositions of n such that the smallest part divides every part.

1, 2, 4, 8, 14, 32, 57, 123, 239, 493, 970, 1997, 3953, 8017, 16024, 32281, 64550, 129742, 259561, 520606, 1041871, 2087177, 4176594, 8362063, 16730862, 33483361, 66987710, 134029333, 268117646, 536373213, 1072909785, 2146169660

Offset: 1

Author

Vladeta Jovovic, Jul 01 2007

Keywords

• easy
• nonn

Examples

			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.
		

Crossrefs

Cf. A083710.

Programs

Maple

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

Formula

Inverse Moebius transform of A099036.

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

Extensions

More terms from Emeric Deutsch, Sep 08 2007