OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 61*x^5 + 257*x^6 + 1153*x^7 + 5417*x^8 + 26409*x^9 + 132812*x^10 + 686158*x^11 + 3631067*x^12 + ...
such that A = A(x) satisfies
A(x) = (1-x)/(1-x*A) + x*(1-x*A^2)/(1-x*A^3) + x^2*(1-x*A^4)/(1-x*A^5) + x^3*(1-x*A^6)/(1-x*A^7) + x^4*(1-x*A^8)/(1-x*A^9) + x^5*(1-x*A^10)/(1-x*A^11) + ...
MATHEMATICA
m = 31; A[_] = 1;
Do[A[x_] = Sum[x^n (1 - x A[x]^(2n))/(1 - x A[x]^(2n + 1)), {n, 0, k}] + O[x]^k, {k, 1, m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 01 2019 *)
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = Vec( sum(n=0, #A, x^n * (1 - x*Ser(A)^(2*n))/(1 - x*Ser(A)^(2*n+1)) ) )); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 29 2019
STATUS
approved