OFFSET
0,4
LINKS
Carles Cardó, Growth and density in free magmas, arXiv:2401.07827 [math.CO], 2024. See p. 16.
FORMULA
G.f.: (1 - sqrt(1 - 2*x + 2*x*sqrt(1 - 4*x)))/(2*x).
a(n) ~ 2^(2*n - 3/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jan 28 2024
D-finite with recurrence n*(n+1)*a(n) -2*n*(7*n-8)*a(n-1) +4*(17*n^2-55*n+39)*a(n-2) +4*(-28*n^2+158*n-213)*a(n-3) +12*(-8*n^2+36*n-25)*a(n-4) +8*(56*n^2-460*n+921)*a(n-5) -16*(4*n-21)*(4*n-23)*a(n-6)=0. - R. J. Mathar, Mar 25 2024
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[1 - 2*x + 2*x*Sqrt[1 - 4*x]])/(2*x), {x, 0, 12}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 25 2024
STATUS
approved