|
|
A156195
|
|
a(2n+2) = 6*a(2n+1), a(2n+1) = 6*a(2n) - 5^n*A000108(n), a(0)=1.
|
|
6
|
|
|
1, 5, 30, 175, 1050, 6250, 37500, 224375, 1346250, 8068750, 48412500, 290343750, 1742062500, 10450312500, 62701875000, 376177734375, 2257066406250, 13541839843750, 81251039062500, 487496738281250, 2924980429687500, 17549718554687500, 105298311328125000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} A120730(n,k)*5^k.
(n+1)*a(n) = 6*(n+1)*a(n-1) + 20*(n-2)*a(n-2) - 120*(n-2)*a(n-3). - R. J. Mathar, Jul 21 2016
|
|
MAPLE
|
option remember;
local nh;
if n= 0 then
1;
elif type(n, 'even') then
6*procname(n-1);
else
nh := floor(n/2) ;
end if;
|
|
MATHEMATICA
|
CoefficientList[Series[(Sqrt[1-20x^2]+10x-1)/(10x(1-6x)), {x, 0, 30}], x] (* Harvey P. Dale, Oct 21 2016 *)
|
|
PROG
|
(Magma) [n le 3 select Factorial(n+3)/24 else (6*n*Self(n-1) + 20*(n-3)*Self(n-2) - 120*(n-3)*Self(n-3))/n: n in [1..30]]; // G. C. Greubel, Nov 09 2022
(SageMath)
if (n==0): return 1
elif (n%2==1): return 6*a(n-1) - 5^((n-1)/2)*catalan_number((n-1)/2)
else: return 6*a(n-1)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|