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%I #10 May 22 2020 04:38:21
%S 1,1,2,4,8,14,26,45,79,137,241,423,754,1343,2410,4344,7870,14305,
%T 26103,47763,87649,161229,297251,549108,1016243,1883898,3497761,
%U 6503420,12107958,22570221,42121298,78692765,147165225,275476533,516115940
%N Number of compositions of n such that every part divides the largest part.
%H Alois P. Heinz, <a href="/A130708/b130708.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 1 + Sum_{n>0} x^n/((1-Sum_{d divides n} x^d)*(1-Sum_{d divides n,d<n} x^d)).
%p A130708 := proc(n) local gf,den1,den2,i,d ; gf := 1 ; for i from 1 to n do den1 := 1 ; den2 := 1 ; for d in numtheory[divisors](i) do den1 := den1-x^d ; if d < i then den2 := den2-x^d ; fi ; od ; gf := taylor(gf+x^i/den1/den2,x=0,n+1) ; od: coeftayl(gf,x=0,n) ; end: seq(A130708(n),n=0..40) ; # _R. J. Mathar_, Oct 28 2007
%t m = 35;
%t 1 + Sum[x^n/((1 - Sum[x^d, {d, Divisors[n]}]) (1 - Sum[Boole[d < n] x^d, {d, Divisors[n]}])), {n, 1, m}] + O[x]^m // CoefficientList[#, x]& (* _Jean-François Alcover_, May 22 2020 *)
%Y Cf. A100346, A018818, A083710, A097986, A117086.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jul 01 2007
%E More terms from _R. J. Mathar_, Oct 28 2007
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