A112807 Expansion of solution of functional equation.

1, 1, 3, 13, 66, 365, 2132, 12940, 80804, 515776, 3350165, 22071930, 147141469, 990714900, 6727506071, 46020535285, 316837676938, 2193700600205, 15265011340106, 106699930507346, 748827090415380, 5274495878205514

Offset

0,3

Links

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

Gi-Sang Cheon, S.-T. Jin, and L. W. Shapiro, A combinatorial equivalence relation for formal power series, Linear Algebra and its Applications, Volume 491, 15 February 2016, Pages 123-137.

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