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A112807 Expansion of solution of functional equation. 0
1, 1, 3, 13, 66, 365, 2132, 12940, 80804, 515776, 3350165, 22071930, 147141469, 990714900, 6727506071, 46020535285, 316837676938, 2193700600205, 15265011340106, 106699930507346, 748827090415380, 5274495878205514 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Gi-Sang Cheon, S.-T. Jin, L. W. Shapiro, A combinatorial equivalence relation for formal power series, Linear Algebra and its Applications, Available online 30 March 2015.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

Given g.f. A(x), then series reversion of B(x)=x*A(x^5) is -B(-x).

Given g.f. A(x), then y=x*A(x^5) satisfies y=x+(xy)^3/(1-(xy)^5).

G.f. satisfies: A(x) = 1 + x*A(x)^3/(1 - x^2*A(x)^5). - Paul D. Hanna, Jun 06 2012

G.f. satisfies: A(x) = 1/A(-x*A(x)^5); note that the function G(x) = 1 + x*G(x)^3 (A001764) also satisfies this condition. - Paul D. Hanna, Jun 06 2012

PROG

(PARI) a(n)=local(A); if(n<0, 0, A=x+O(x^6); for(k=1, n, A=x+subst(x^3/(1-x^5), x, x*A)); polcoeff(A, 5*n+1))

(PARI) a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*A^3/(1-x^2*A^5)); polcoeff(A, n) \\ Paul D. Hanna, Jun 06 2012

CROSSREFS

Sequence in context: A156181 A260783 A228987 * A219537 A045743 A110530

Adjacent sequences:  A112804 A112805 A112806 * A112808 A112809 A112810

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 20 2005

STATUS

approved

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Last modified May 9 13:09 EDT 2021. Contains 343742 sequences. (Running on oeis4.)