cp's OEIS Frontend

A179487 G.f. satisfies: A(x)^(1/3) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +... where A(x) = Sum_{n>=1} a(n)*x^(2n-1).

%I A179487 #2 Mar 30 2012 18:37:22
%S A179487 1,3,12,55,276,1470,8160,46692,273450,1631091,9874836,60522111,
%T A179487 374783066,2341345848,14738239920,93389126442,595210710006,
%U A179487 3813127548837,24540706889124,158592962937843,1028721051285840
%N A179487 G.f. satisfies: A(x)^(1/3) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +... where A(x) = Sum_{n>=1} a(n)*x^(2n-1).
%e A179487 G.f.: A(x) = x^3 + 3*x^5 + 12*x^7 + 55*x^9 + 276*x^11 + 1470*x^13 +...
%e A179487 A(x)^(1/3) = x + x^3 + 3*x^5 + 12*x^7 + 56*x^9 + 285*x^11 +...
%e A179487 Related expansions:
%e A179487 A(A(x)) = x^9 + 9*x^11 + 63*x^13 + 411*x^15 + 2619*x^17 + 16569*x^19 +..
%e A179487 A(A(A(x))) = x^27 + 27*x^29 + 432*x^31 + 5364*x^33 + 57267*x^35 +...
%e A179487 A(A(A(A(x)))) = x^81 + 81*x^83 + 3483*x^85 + 105759*x^87 +...
%e A179487 where A(x)^(1/3) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +...
%o A179487 (PARI) {a(n)=local(A=x+x^3); for(i=0, n, A=serreverse(x-subst(A, x, x^3+x^2*O(x^(2*n))))); polcoeff(A^3, 2*n-1)}
%Y A179487 Cf. A179486, A141201 (variant).
%K A179487 nonn
%O A179487 3,2
%A A179487 _Paul D. Hanna_, Aug 12 2010