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Number of compositions of n such that the largest part is coprime to every other part.
1

%I #6 Aug 24 2015 02:36:48

%S 1,1,2,4,7,13,22,41,75,138,255,482,911,1735,3316,6370,12306,23907,

%T 46666,91500,180119,355820,705061,1400722,2788718,5561720,11107305,

%U 22205839,44429088,88942741,178120533,356787834,714732794,1431763102,2867860060

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

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

%p 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

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, Jul 01 2007

%E More terms from _R. J. Mathar_, Oct 28 2007