OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 3 / (3 + x * A(x) - 4 * x * A(4*x)).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/3) Sum[(4^k - 1) a[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 13}]
nmax = 13; A[_] = 0; Do[A[x_] = 3/(3 + x A[x] - 4 x A[4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 10 2024
STATUS
approved