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%I #3 Jun 20 2019 22:44:42
%S 1,5,40,1185,65270,4861126,445776670,48124064710,5952881626790,
%T 828544320379330,128058593506875627,21758230559633783765,
%U 4031357498037096661170,809070343591564791211705,174888309616496370413590235,40517215307075701804767255261,10017278630199891781122121185615,2632883558256463087445119555912870,733167697272377998186394054589647855,215641985221691590110546294934099963285
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(5*n) - A(x) )^n.
%F G.f. A(x) satisfies:
%F (1) 1 = Sum_{n>=0} ( 1/(1-x)^(5*n) - A(x) )^n.
%F (2) 1 = Sum_{n>=0} ( 1 - (1-x)^(5*n)*A(x) )^n / (1-x)^(5*n^2).
%F (3) 1 = Sum_{n>=0} (1-x)^(5*n) / ( (1-x)^(5*n) + A(x) )^(n+1).
%e G.f.: A(x) = 1 + 5*x + 40*x^2 + 1185*x^3 + 65270*x^4 + 4861126*x^5 + 445776670*x^6 + 48124064710*x^7 + 5952881626790*x^8 + 828544320379330*x^9 + 128058593506875627*x^10 + ...
%e such that
%e 1 = 1 + (1/(1-x)^5 - A(x)) + (1/(1-x)^10 - A(x))^2 + (1/(1-x)^15 - A(x))^3 + (1/(1-x)^20 - A(x))^4 + (1/(1-x)^25 - A(x))^5 + (1/(1-x)^30 - A(x))^6 + (1/(1-x)^35 - A(x))^7 + ...
%e Also,
%e 1 = 1/(1 + A(x)) + (1-x)^5/((1-x)^5 + A(x))^2 + (1-x)^10/((1-x)^10 + A(x))^3 + (1-x)^15/((1-x)^15 + A(x))^4 + (1-x)^20/((1-x)^20 + A(x))^5 + (1-x)^25/((1-x)^25 + A(x))^6 + (1-x)^30/((1-x)^30 + A(x))^7 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ((1-x)^(-5*m) - Ser(A))^m ) )[#A] ); H=A; A[n+1]}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A304639, A326262, A326263, A326264.
%Y Cf. A321605.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 20 2019
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