The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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