|
|
A305032
|
|
a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 4*a(n-2) for n > 1.
|
|
2
|
|
|
0, 1, 6, 22, 68, 190, 500, 1260, 3080, 7350, 17220, 39732, 90552, 204204, 456456, 1012440, 2230800, 4886310, 10647780, 23094500, 49884120, 107343236, 230205976, 492156392, 1049212528, 2230928700, 4732273000, 10015777800, 21154820400, 44596287000, 93846099600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
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
if n<2: return n
else: return 2*(3*a(n-1) + 2*(n-1)*a(n-2))//(n-1)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|