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A190761
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G.f. satisfies: A(x) = x + A(A(x))^2 - A(A(x))^3.
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4
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1, 1, 3, 14, 84, 592, 4670, 40108, 368670, 3586321, 36632763, 390694000, 4332131804, 49777965585, 591173511887, 7241437905916, 91331043654080, 1184322726542850, 15770586926609276, 215423253906689779, 3015794930248824111, 43233248160139146114
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OFFSET
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1,3
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COMMENTS
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Compare to a formula for a g.f. of the Catalan numbers (A000108):
C(x) = x + C(x)*C(C(x)) - C(x)*C(C(x))^2 where C(x) = (1-sqrt(1-4*x))/2.
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LINKS
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Table of n, a(n) for n=1..22.
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FORMULA
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G.f. satisfies: A( x - A(x)^2 + A(x)^3 ) = x.
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EXAMPLE
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G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 84*x^5 + 592*x^6 + 4670*x^7 +...
Related series begin:
A(A(x)) = x + 2*x^2 + 8*x^3 + 44*x^4 + 294*x^5 + 2244*x^6 + 18888*x^7 +...
A(A(x))^2 = x^2 + 4*x^3 + 20*x^4 + 120*x^5 + 828*x^6 + 6368*x^7 +...
A(A(x))^3 = x^3 + 6*x^4 + 36*x^5 + 236*x^6 + 1698*x^7 +...
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PROG
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(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=serreverse(x-A^2+A^3+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Sequence in context: A074535 A256337 A256330 * A005700 A220911 A088717
Adjacent sequences: A190758 A190759 A190760 * A190762 A190763 A190764
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, May 18 2011
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STATUS
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approved
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