A179487 - OEIS

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

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OFFSET

3,2

LINKS

Table of n, a(n) for n=3..23.

EXAMPLE

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)))) +...

PROG

(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)}

CROSSREFS

Cf. A179486, A141201 (variant).

Sequence in context: A366100 A342283 A120920 * A350265 A263533 A064314

Adjacent sequences: A179484 A179485 A179486 * A179488 A179489 A179490

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 12 2010

STATUS

approved