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A326262 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(2*n) - A(x) )^n.

%I A326262 #3 Jun 20 2019 22:39:38
%S A326262 1,2,7,80,1742,51842,1902589,82219592,4071164749,226803165574,
%T A326262 14029472009781,953926536359084,70723894649169937,5679305945331227594,
%U A326262 491179287055641264989,45527108214667404725616,4503148842172835722939285,473502491643614888369261116,52748299277043902326373361722,6206479798643382507763241117360,769187266152748793100664986340382,100156538984193022704291755068539370
%N A326262 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(2*n) - A(x) )^n.
%F A326262 G.f. A(x) satisfies:
%F A326262 (1) 1 = Sum_{n>=0} ( 1/(1-x)^(2*n) - A(x) )^n.
%F A326262 (2) 1 = Sum_{n>=0} ( 1 - (1-x)^(2*n)*A(x) )^n / (1-x)^(2*n^2).
%F A326262 (3) 1 = Sum_{n>=0} (1-x)^(2*n) / ( (1-x)^(2*n) + A(x) )^(n+1).
%e A326262 G.f.: A(x) = 1 + 2*x + 7*x^2 + 80*x^3 + 1742*x^4 + 51842*x^5 + 1902589*x^6 + 82219592*x^7 + 4071164749*x^8 + 226803165574*x^9 + 14029472009781*x^10 + ...
%e A326262 such that
%e A326262 1 = 1  +  (1/(1-x)^2 - A(x))  +  (1/(1-x)^4 - A(x))^2  +  (1/(1-x)^6 - A(x))^3  +  (1/(1-x)^8 - A(x))^4  +  (1/(1-x)^10 - A(x))^5  +  (1/(1-x)^12 - A(x))^6  +  (1/(1-x)^14 - A(x))^7  + ...
%e A326262 Also,
%e A326262 1 = 1/(1 + A(x))  +  (1-x)^2/((1-x)^2 + A(x))^2  +  (1-x)^4/((1-x)^4 + A(x))^3  +  (1-x)^6/((1-x)^6  +  A(x))^4 + (1-x)^8/((1-x)^8 + A(x))^5  +  (1-x)^10/((1-x)^10 + A(x))^6  +  (1-x)^12/((1-x)^12 + A(x))^7 + ...
%o A326262 (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) - Ser(A))^m ) )[#A] ); H=A; A[n+1]}
%o A326262 for(n=0, 30, print1(a(n), ", "))
%Y A326262 Cf. A304639, A326263, A326264, A326265.
%Y A326262 Cf. A321602.
%K A326262 nonn
%O A326262 0,2
%A A326262 _Paul D. Hanna_, Jun 20 2019