A130709 Number of compositions of n such that the largest part is coprime to every other part.

1, 1, 2, 4, 7, 13, 22, 41, 75, 138, 255, 482, 911, 1735, 3316, 6370, 12306, 23907, 46666, 91500, 180119, 355820, 705061, 1400722, 2788718, 5561720, 11107305, 22205839, 44429088, 88942741, 178120533, 356787834, 714732794, 1431763102, 2867860060

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: 1/(1-x) + Sum_{n>1} x^n/(1-Sum_{d | 1<=d<=n, gcd(n,d)=1} x^d)^2.

Maple

A130709 := proc(n) local gf, den, i, d ; gf := 0 ; for i from 2 to n do den := 1 ; for d from 1 to i-1 do if gcd(d, i) = 1 then den := den-x^d ; fi ; od ; gf := taylor(gf+x^i/den^2, x=0, n+1) ; od: 1+coeftayl(gf, x=0, n) ; end: seq(A130709(n), n=0..40) ; # R. J. Mathar, Oct 28 2007

Crossrefs

Sequence in context: A254007 A001036 A054150 * A051013 A128609 A335471

Adjacent sequences: A130706 A130707 A130708 * A130710 A130711 A130712

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 01 2007

Extensions

More terms from R. J. Mathar, Oct 28 2007

Status

approved