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Write x/(1-x) in the form Sum_{j>=1} a(j)*x^j/(1+a(j)*x^j).
9

%I #9 Aug 27 2017 23:13:03

%S 1,2,0,6,0,-6,0,54,0,-30,0,-114,0,-126,0,4470,0,-294,0,-5850,0,-2046,

%T 0,-92418,0,-8190,0,-247674,0,2010,0,30229110,0,-131070,0,-8200914,0,

%U -524286,0,-362617770,0,183162,0,-354416634,0,-8388606,0,-53614489794,0

%N Write x/(1-x) in the form Sum_{j>=1} a(j)*x^j/(1+a(j)*x^j).

%F a(n) = -Sum_t (-1)^v(t) where the sum is over all same-trees of weight n (see A281145 for definition) and v(t) is the number of nodes (branchings and leaves) in t.

%t nn=20;-Solve[Table[Sum[a[n/d]^d,{d,Divisors[n]}]==-1,{n,nn}],Array[a,nn]][[1,All,2]]

%Y Cf. A048272, A220418, A260685, A273873, A275870, A281145, A289078, A289501, A290261, A290973.

%K sign

%O 1,2

%A _Gus Wiseman_, Aug 16 2017