OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x + 5 * (x * A(x))^2.
G.f.: (1 - sqrt(1 - 20 * x^2 * (1 + x))) / (10 * x^2).
a(n) ~ sqrt((2+3*r)*(1+r)) / (sqrt(Pi) * n^(3/2) * r^n), where r = 2*cos(arccos(-13/40)/3)/3 - 1/3. - Vaclav Kotesovec, Jun 04 2022
MATHEMATICA
a[0] = a[1] = 1; a[n_] := a[n] = 5 Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
nmax = 26; CoefficientList[Series[(1 - Sqrt[1 - 20 x^2 (1 + x)])/(10 x^2), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 04 2022
STATUS
approved