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A325154 G.f. A(x) satisfies: 1 = Sum_{n>=0} ((1+x)^(2*n-1) - A(x))^n.

%I A325154 #3 Apr 12 2019 00:29:02
%S A325154 1,1,4,60,1349,40210,1470027,63225750,3116555468,172936040306,
%T A325154 10661699020596,722933543336296,53476543241702021,4286318739039468220,
%U A325154 370139507278333619231,34264675353237245461705,3385595826616475280589858,355676742010175185149150523,39592541401227701053287450374,4655516336942715288212969823798,576645913391345319618489456738288,75048370900002385430200781452328814
%N A325154 G.f. A(x) satisfies: 1 = Sum_{n>=0} ((1+x)^(2*n-1) - A(x))^n.
%F A325154 G.f. A(x) satisfies:
%F A325154 (1) 1 = Sum_{n>=0} ((1+x)^(2*n-1) - A(x))^n.
%F A325154 (2) 1 = Sum_{n>=0} (1+x)^(2*n^2-n) / (1 + (1+x)^(2*n)*A(x))^(n+1).
%e A325154 G.f.: A(x) = 1 + x + 4*x^2 + 60*x^3 + 1349*x^4 + 40210*x^5 + 1470027*x^6 + 63225750*x^7 + 3116555468*x^8 + 172936040306*x^9 + 10661699020596*x^10 + ...
%e A325154 such that
%e A325154 1 = 1  +  ((1+x) - A(x))  +  ((1+x)^3 - A(x))^2  +  ((1+x)^5 - A(x))^3  +  ((1+x)^7 - A(x))^4  +  ((1+x)^9 - A(x))^5  +  ((1+x)^11 - A(x))^6  +  ((1+x)^13 - A(x))^7 + ...
%e A325154 Also,
%e A325154 1 = 1/(1 + A(x))  +  (1+x)/(1 + (1+x)^2*A(x))^2  +  (1+x)^6/(1 + (1+x)^4*A(x))^3  +  (1+x)^15/(1 + (1+x)^6*A(x))^4  +  (1+x)^28/(1 + (1+x)^8*A(x))^5  +  (1+x)^45/(1 + (1+x)^10*A(x))^6  +  (1+x)^66/(1 + (1+x)^6*A(x))^7 + ...
%o A325154 (PARI) {a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ((1+x)^(2*m-1) - Ser(A))^m ) )[#A] ); A[n+1]}
%o A325154 for(n=0, 30, print1(a(n), ", "))
%Y A325154 Cf. A303056.
%K A325154 nonn
%O A325154 0,3
%A A325154 _Paul D. Hanna_, Apr 12 2019