OFFSET
1,4
FORMULA
Series reversion of g.f. A(x) is -A(-x).
Given g.f. A(x) and B(x) = g.f. of A089796, then B(x)=x+A(x*B(x)).
G.f. A(x)=y satisfies 0=y^3+(-x-1)*y^2+(x^2+3*x-1)*y+(-x^3-x^2+x).
D-finite with recurrence 5*n*(n-1)*(6947*n-150973)*a(n) +(n-1)*(909994*n^2 -5636597*n +10466184)*a(n-1) +(-3594151*n^3 +36668949*n^2 -116071772*n +115774518)*a(n-2) +(3752530*n^3 -43272273*n^2 +163807289*n -203448234)*a(n-3) +(-5236321*n^3 +69827238*n^2 -307215935*n +448390974)*a(n-4) +4*(1072898*n^3 -16156263*n^2 +76788526*n -112806741)*a(n-5) -48*(n-7) *(36817*n^2 -393746*n +906725)*a(n-6) -256*(12938*n-42081) *(n-7)*(n-8) *a(n-7)=0. - R. J. Mathar, Jul 20 2023
PROG
(PARI) {a(n)=local(A); if(n<1, 0, A=O(x); for(k=1, n, A=A^3+(-x-1)*A^2+(x^2+3*x)*A+(-x^3-x^2+x)); polcoeff(A, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 08 2005
STATUS
approved