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A326263 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(3*n) - A(x) )^n.

%I A326263 #3 Jun 20 2019 22:41:32
%S A326263 1,3,15,262,8616,384873,21181421,1372455324,101895990777,
%T A326263 8511828635054,789539638329648,80506096148928303,8951189588697000825,
%U A326263 1078020157296224938479,139830500253903232730304,19438947952499889395212003,2883820412306778479104733811,454810046719340404484233328331,75993667094400965507408118716882,13411571696501962452150617362998648,2493074269436929464139674369969509811
%N A326263 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(3*n) - A(x) )^n.
%F A326263 G.f. A(x) satisfies:
%F A326263 (1) 1 = Sum_{n>=0} ( 1/(1-x)^(3*n) - A(x) )^n.
%F A326263 (2) 1 = Sum_{n>=0} ( 1 - (1-x)^(3*n)*A(x) )^n / (1-x)^(3*n^2).
%F A326263 (3) 1 = Sum_{n>=0} (1-x)^(3*n) / ( (1-x)^(3*n) + A(x) )^(n+1).
%e A326263 G.f.: A(x) = 1 + 3*x + 15*x^2 + 262*x^3 + 8616*x^4 + 384873*x^5 + 21181421*x^6 + 1372455324*x^7 + 101895990777*x^8 + 8511828635054*x^9 + 789539638329648*x^10 + ...
%e A326263 such that
%e A326263 1 = 1  +  (1/(1-x)^3 - A(x))  +  (1/(1-x)^6 - A(x))^2  +  (1/(1-x)^9 - A(x))^3  +  (1/(1-x)^12 - A(x))^4  +  (1/(1-x)^15 - A(x))^5  +  (1/(1-x)^18 - A(x))^6  +  (1/(1-x)^21 - A(x))^7  + ...
%e A326263 Also,
%e A326263 1 = 1/(1 + A(x))  +  (1-x)^3/((1-x)^3 + A(x))^2  +  (1-x)^6/((1-x)^6 + A(x))^3  +  (1-x)^9/((1-x)^9  +  A(x))^4 + (1-x)^12/((1-x)^12 + A(x))^5  +  (1-x)^15/((1-x)^15 + A(x))^6  +  (1-x)^18/((1-x)^18 + A(x))^7 + ...
%o A326263 (PARI) {a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ((1-x)^(-3*m) - Ser(A))^m ) )[#A] ); H=A; A[n+1]}
%o A326263 for(n=0, 30, print1(a(n), ", "))
%Y A326263 Cf. A304639, A326262, A326264, A326265.
%Y A326263 Cf. A321603.
%K A326263 nonn
%O A326263 0,2
%A A326263 _Paul D. Hanna_, Jun 20 2019