OFFSET
0,3
FORMULA
G.f.: (1 - 2*x - x^2 - sqrt(1 - 4*x - 2*x^2 + 8*x^3 + x^4)) / (2*x^2).
a(0) = a(1) = 1; a(n) = 2 * a(n-1) + a(n-2) + Sum_{k=0..n-2} a(k) * a(n-k-2).
MATHEMATICA
nmax = 28; A[_] = 0; Do[A[x_] = (1 - x)/(1 - 2 x - x^2 - x^2 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 28; CoefficientList[Series[(1 - 2 x - x^2 - Sqrt[1 - 4 x - 2 x^2 + 8 x^3 + x^4])/(2 x^2), {x, 0, nmax}], x]
a[0] = a[1] = 1; a[n_] := a[n] = 2 a[n - 1] + a[n - 2] + Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 09 2021
STATUS
approved