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A154677
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G.f. satisfies: A(x/A(x)) = G(x) where G(x) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan numbers).
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5
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1, 1, 3, 13, 70, 440, 3116, 24274, 204407, 1836339, 17425275, 173329307, 1796783304, 19323703019, 214843877103, 2462522274426, 29032815570544, 351447240945518, 4361579736404011, 55424256247911490, 720399315622779670
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. satisfies: A( (x-x^2)/A(x-x^2) ) = 1/(1-x).
G.f. satisfies: A( (x/(1+x)^2)/A(x/(1+x)^2) ) = 1 + x.
G.f. satisfies: A(x) = 1 + A(x)^2*Series_Reversion(x/A(x)). [From Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2009]
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EXAMPLE
| G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 70*x^4 + 440*x^5 +... where
A(x/A(x)) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
x/A(x) = x - x^2 - 2*x^3 - 8*x^4 - 43*x^5 - 277*x^6 - 2026*x^7 -...
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PROG
| (PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(2*k+1, k)/(2*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F, x, serreverse(x/(A+x*O(x^n))))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+A^2*serreverse(x/(A+x*O(x^n)))); polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2009]
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CROSSREFS
| Cf. A000108.
Cf. variants: A154677, A168448, A168478. [From Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2009]
Sequence in context: A119906 A059726 A192209 * A121586 A024337 A001495
Adjacent sequences: A154674 A154675 A154676 * A154678 A154679 A154680
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 14 2009
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