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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
OFFSET
0,3
LINKS
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: A260783 A373932 A228987 * A219537 A045743 A110530
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 20 2005
STATUS
approved