OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 3 * x^2 * A'(x) - x^3 * A''(x)) ).
MATHEMATICA
a[n_] := a[n] = 1 + Sum[(k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 3 x^2 A'[x] - x^3 A''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2024
STATUS
approved