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A112807 Expansion of solution of functional equation. 0

%I

%S 1,1,3,13,66,365,2132,12940,80804,515776,3350165,22071930,147141469,

%T 990714900,6727506071,46020535285,316837676938,2193700600205,

%U 15265011340106,106699930507346,748827090415380,5274495878205514

%N Expansion of solution of functional equation.

%D 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.

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

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

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

%F 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

%o (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))

%o (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

%K nonn

%O 0,3

%A _Michael Somos_, Sep 20 2005

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)