OFFSET
0,3
COMMENTS
Let a(0) = 0, a(1) = 1 and a(n) = 2*m*a(n-1)/(n-1) + k^2*a(n-2), for n > 1, then the g.f. is x/(2*m) * d/dx ((1 + k*x)/(1 - k*x))^(m/k).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3000
FORMULA
a(n) = n*A305031(n)/6.
G.f.: x*sqrt(1-4*x^2)/(1-2*x)^3.
MATHEMATICA
CoefficientList[Series[x*Sqrt[1-4*x^2]/(1-2*x)^3, {x, 0, 40}], x] (* G. C. Greubel, Jun 07 2023 *)
PROG
(Magma) [n le 2 select n-1 else 2*(3*Self(n-1) + 2*(n-2)*Self(n-2))/(n-2): n in [1..40]]; // G. C. Greubel, Jun 07 2023
(SageMath)
@CachedFunction
def a(n): # b = A305032
if n<2: return n
else: return 2*(3*a(n-1) + 2*(n-1)*a(n-2))//(n-1)
[a(n) for n in range(41)] # G. C. Greubel, Jun 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 24 2018
STATUS
approved