A326264 - OEIS

%I #3 Jun 20 2019 22:42:46

%S 1,4,26,612,26919,1603680,117660064,10162944112,1005838347950,

%T 112009295740916,13850874442895434,1882848486231714788,

%U 279100448753985866813,44813411860476850508720,7749809454081027489860264,1436399220794697421878462832,284111046278259235057207651469,59740768193467931633275499487660,13308884562229489858971683010469182,3131623636896229572958776700673759164

%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1/(1-x)^(4*n) - A(x) )^n.

%F G.f. A(x) satisfies:

%F (1) 1 = Sum_{n>=0} ( 1/(1-x)^(4*n) - A(x) )^n.

%F (2) 1 = Sum_{n>=0} ( 1 - (1-x)^(4*n)*A(x) )^n / (1-x)^(4*n^2).

%F (3) 1 = Sum_{n>=0} (1-x)^(4*n) / ( (1-x)^(4*n) + A(x) )^(n+1).

%e G.f.: A(x) = 1 + 4*x + 26*x^2 + 612*x^3 + 26919*x^4 + 1603680*x^5 + 117660064*x^6 + 10162944112*x^7 + 1005838347950*x^8 + 112009295740916*x^9 + 13850874442895434*x^10 + ...

%e such that

%e 1 = 1  +  (1/(1-x)^4 - A(x))  +  (1/(1-x)^8 - A(x))^2  +  (1/(1-x)^12 - A(x))^3  +  (1/(1-x)^16 - A(x))^4  +  (1/(1-x)^20 - A(x))^5  +  (1/(1-x)^24 - A(x))^6  +  (1/(1-x)^28 - A(x))^7  + ...

%e Also,

%e 1 = 1/(1 + A(x))  +  (1-x)^4/((1-x)^4 + A(x))^2  +  (1-x)^8/((1-x)^8 + A(x))^3  +  (1-x)^12/((1-x)^12  +  A(x))^4 + (1-x)^16/((1-x)^16 + A(x))^5  +  (1-x)^20/((1-x)^20 + A(x))^6  +  (1-x)^24/((1-x)^24 + 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)^(-4*m) - Ser(A))^m ) )[#A] ); H=A; A[n+1]}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A304639, A326262, A326263, A326265.

%Y Cf. A321604.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 20 2019