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A130711
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Number of compositions of n such that the smallest part divides every part.
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0
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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; internal format)
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OFFSET
| 1,2
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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)).
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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.
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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 (deutsch(AT)duke.poly.edu), Sep 08 2007
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CROSSREFS
| Cf. A083710.
Sequence in context: A118560 A038024 A061297 * A093483 A028398 A155249
Adjacent sequences: A130708 A130709 A130710 * A130712 A130713 A130714
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 01 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 08 2007
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