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A153305
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G.f. satisfies: A(x) = x + 3*x*A(x) + 6*x*A(x)*A(A(x)) + 10*x*A(x)*A(A(x))*A(A(A(x))) +...
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0
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1, 3, 15, 109, 1008, 10983, 135097, 1828425, 26777775, 419530384, 6973851684, 122248585620, 2249238083514, 43274933036838, 868047525689328, 18108325893968859, 392039367345646323, 8792515088387598651
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OFFSET
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0,2
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LINKS
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FORMULA
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x = A(x) - 3*x*A(A(x)) + 3*x*A(x)*A(A(A(x))) - x*A(x)*A(A(x))*A(A(A(A(x)))).
A(x) = x*(1 + 3*A(A(x)))/(1 + 3*x*A(A(A(x))) - x*A(A(x))*A(A(A(A(x))))).
A(x) = Series_Reversion[x/(1 + 3*A(x) - 3*x*A(A(x)) + x*A(x)*A(A(A(x))))].
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EXAMPLE
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G.f.: A(x) = x + 3*x^2 + 15*x^3 + 109*x^4 + 1008*x^5 + 10983*x^6 +...
A(A(x)) = x + 6*x^2 + 48*x^3 + 470*x^4 + 5328*x^5 + 67557*x^6 +...
A(A(A(x))) = x + 9*x^2 + 99*x^3 + 1245*x^4 + 17280*x^5 + 259362*x^6 +...
A(A(A(A(x))) = x + 12*x^2 + 168*x^3 + 2596*x^4 + 43128*x^5 + 759306*x^6 +...
A(A(A(A(A(x)))) = x + 15*x^2 + 255*x^3 + 4685*x^4 + 91080*x^5 +...
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PROG
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(PARI) {a(n)=local(A=x+x*O(x), B, C); for(i=1, n, B=subst(A, x, A); C=subst(A, x, B); A=serreverse(x/(1+3*A-3*x*B+x*A*C))); polcoeff(A, n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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