A138208 - OEIS

%I #7 Sep 26 2024 23:16:44

%S 1,1,-1,4,-28,281,-3684,59731,-1154936,25950691,-664613080,

%T 19112126640,-609797430996,21378439099625,-816913146902756,

%U 33793354034365895,-1504592807223959688,71739597692510725317,-3647111535920547933017

%N G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(-2n+1))...)^-5)^-3)^-1.

%e G.f.: A(x)=1+x/B(x), B(x)=1+x/C(x)^3, C(x)=1+x/D(x)^5, D(x)=1+x/E(x)^7, ...

%e where A(x),B(x),C(x),... are the g.f. of the sequences given below.

%e A=[1,1,-1,4,-28,281,-3684,59731,-1154936,25950691,...];

%e B=[1,1,-3,21,-220,3015,-50721,1009311,-23180763,603647340,...];

%e C=[1,1,-5,50,-700,12250,-254086,6060285,-163013950,4877935870,...];

%e D=[1,1,-7,91,-1596,34062,-843003,23549442,-730039689,24824392005,...];

%e E=[1,1,-9,144,-3036,76527,-2204136,70735467,-2490112548,95152481622,...];

%e F=[1,1,-11,209,-5148,149721,-4923061,178674925,-7052351735,...]; ...

%o (PARI) {a(n)=my(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x/A^(2*(n-j)-1)); polcoeff(A, n)}

%Y Cf. A121587, A138211, A138210, A138209.

%K sign

%O 0,4

%A _Paul D. Hanna_, Mar 06 2008