A112482 Expansion of the solution of a functional equation.

1, 1, 1, 2, 4, 8, 17, 38, 87, 203, 482, 1160, 2822, 6930, 17157, 42775, 107300, 270623, 685842, 1745651, 4460450, 11437423, 29421695, 75906148, 196358971, 509209381, 1323524122, 3447340550, 8996802898, 23522607256, 61606041763, 161604774963

Offset

1,4

Links

Table of n, a(n) for n=1..32.

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

Sequence in context: A114199 A006196 A089796 * A193050 A107597 A082499

Adjacent sequences: A112479 A112480 A112481 * A112483 A112484 A112485

Keyword

nonn

Author

Michael Somos, Sep 08 2005

Status

approved