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A229619
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G.f. satisfies: A(x) = Series_Reversion(x - x^2*A’(x)).
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0
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1, 1, 4, 27, 248, 2822, 37820, 578915, 9918924, 187558638, 3873705128, 86692262942, 2089070253556, 53925007946392, 1484529898970648, 43421639185592359, 1344923240469786704, 43981996770022295714, 1514531024603022580980, 54783958839510354056018, 2077007174758224026216216
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..21.
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FORMULA
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G.f. satisfies: A(x) = x + A(x)^2 * A’(A(x))).
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EXAMPLE
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G.f.: A(x) = x + x^2 + 4*x^3 + 27*x^4 + 248*x^5 + 2822*x^6 +...
By definition, A(x - x^2*A’(x)) = x, where
A’(x) = 1 + 2*x + 12*x^2 + 108*x^3 + 1240*x^4 + 16932*x^5 +...
Related expansions.
A'(A(x)) = 1 + 2*x + 14*x^2 + 140*x^3 + 1726*x^4 + 24752*x^5 +...
A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 62*x^5 + 566*x^6 + 6356*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-x^2*A'+x*O(x^n))); polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
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CROSSREFS
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Sequence in context: A212559 A265268 A121063 * A051863 A000699 A138423
Adjacent sequences: A229616 A229617 A229618 * A229620 A229621 A229622
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Sep 26 2013
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STATUS
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approved
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