cp's OEIS Frontend

A228711 G.f. A(x) satisfies: A(x)^4 = A(x^2)^2 + 8*x.

%I A228711 #8 Aug 31 2013 00:33:05
%S A228711 1,2,-5,22,-115,646,-3822,23496,-148368,955822,-6256273,41480668,
%T A228711 -277954706,1879118354,-12800031737,87758481546,-605091552753,
%U A228711 4192829686338,-29180958305391,203887504096188,-1429568781831693,10055261467844862,-70929518958227340
%N A228711 G.f. A(x) satisfies: A(x)^4 = A(x^2)^2 + 8*x.
%F A228711 G.f. A(x) satisfies:
%F A228711 (1) A(x) = sqrt(1/G(x^2)^2 + 4*x*G(x^2)^2),
%F A228711 (2) sqrt(A(x^2)^2 + 4*x) = 1/G(x^4) + 2*x*G(x^4),
%F A228711 where G(x) is the g.f. of A228712.
%F A228711 Self-convolution of A223026.
%e A228711 G.f.: A(x) = 1 + 2*x - 5*x^2 + 22*x^3 - 115*x^4 + 646*x^5 - 3822*x^6 +...
%e A228711 where A(x)^4 = A(x^2)^2 + 8*x as demonstrated by:
%e A228711 A(x)^2 = 1 + 4*x - 6*x^2 + 24*x^3 - 117*x^4 + 612*x^5 - 3426*x^6 + 20184*x^7 +...
%e A228711 A(x)^4 = 1 + 8*x + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +...
%e A228711 The g.f. of A228712 begins:
%e A228711 G(x) = 1 + 3*x + 72*x^2 + 2307*x^3 + 86295*x^4 + 3513477*x^5 +...
%e A228711 and satisfies: sqrt(1/G(x^2)^2 + 4*x*G(x^2)^2) = A(x).
%o A228711 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2)^2+8*x+x*O(x^n))^(1/4)); polcoeff(A, n, x)}
%o A228711 for(n=0, 20, print1(a(n), ", "))
%Y A228711 Cf. A228712, A107086, A223026.
%K A228711 sign
%O A228711 0,2
%A A228711 _Paul D. Hanna_, Aug 30 2013