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).

1, 3, 12, 55, 276, 1470, 8160, 46692, 273450, 1631091, 9874836, 60522111, 374783066, 2341345848, 14738239920, 93389126442, 595210710006, 3813127548837, 24540706889124, 158592962937843, 1028721051285840

Offset: 3

Author

Paul D. Hanna, Aug 12 2010

Keywords

• nonn

Examples

			G.f.: A(x) = x^3 + 3*x^5 + 12*x^7 + 55*x^9 + 276*x^11 + 1470*x^13 +...
A(x)^(1/3) = x + x^3 + 3*x^5 + 12*x^7 + 56*x^9 + 285*x^11 +...
Related expansions:
A(A(x)) = x^9 + 9*x^11 + 63*x^13 + 411*x^15 + 2619*x^17 + 16569*x^19 +..
A(A(A(x))) = x^27 + 27*x^29 + 432*x^31 + 5364*x^33 + 57267*x^35 +...
A(A(A(A(x)))) = x^81 + 81*x^83 + 3483*x^85 + 105759*x^87 +...
where A(x)^(1/3) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +...
		

Crossrefs

Cf. A179486, A141201 (variant).

Programs

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)}