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A130711 Number of compositions of n such that the smallest part divides every part. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

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)).

EXAMPLE

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.

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

CROSSREFS

Cf. A083710.

Sequence in context: A187813 A038024 A061297 * A093483 A028398 A155249

Adjacent sequences:  A130708 A130709 A130710 * A130712 A130713 A130714

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 01 2007

EXTENSIONS

More terms from Emeric Deutsch, Sep 08 2007

STATUS

approved

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Last modified July 14 15:44 EDT 2020. Contains 335729 sequences. (Running on oeis4.)