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A143046
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G.f. satisfies: A(x) = 1 + x*A(-x)^3.
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4
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1, 1, -3, -6, 35, 87, -588, -1578, 11511, 32223, -245883, -706824, 5556564, 16267508, -130617600, -387533058, 3161190783, 9474886287, -78241316361, -236394953670, 1971270824859, 5994591989967, -50388913722480, -154052058035736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^3)^3.
G.f. satisfies: [A(x)^4 + A(-x)^4]/2 = [A(x)^3 + A(-x)^3]/2.
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EXAMPLE
| A(x) = 1 + 3*x - 6*x^2 - 35*x^3 + 87*x^4 + 588*x^5 - 1578*x^6 - 11511*x^7 +...
A(x)^3 = 1 + 3*x - 6*x^2 - 35*x^3 + 87*x^4 + 588*x^5 - 1578*x^6 - 11511*x^7 +...
A(x)^4 = 1 + 4*x - 6*x^2 - 56*x^3 + 87*x^4 + 1008*x^5 - 1578*x^6 - 20464*x^7 +...
Note that a bisction of A^4 equals a bisection of A^3.
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PROG
| (PARI) a(n)=local(A=x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, -x)^3); polcoeff(A, n)
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CROSSREFS
| Cf. A143045, A143046, A143047, A143048, A143049.
Sequence in context: A203715 A134748 A068904 * A009197 A205336 A184390
Adjacent sequences: A143043 A143044 A143045 * A143047 A143048 A143049
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2008
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