OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = ((7*n^2 - 4*n + 1)*a(n-1) + 2*n*(2*n-1)*a(n-2))/(2*(n^2-1)), with a(0) = 1, a(1) = 5, a(2) = 20. - G. C. Greubel, Jul 01 2024
MATHEMATICA
a[n_]:= a[n]= If[n<4, (5*4^(n-1) -Boole[n==1])/4, ((7*n^2-4*n+1)*a[n- 1] +2*n*(2*n-1)*a[n-2])/(2*(n^2-1))];
Table[a[n], {n, 40}] (* G. C. Greubel, Jul 01 2024 *)
PROG
(Magma)
[1] cat [n le 2 select 5*(3*n-2) else ((7*n^2+10*n+4)*Self(n-1) + 2*(2*n+1)*(n+1)*Self(n-2))/(2*n*(n+2)): n in [1..40]]; // G. C. Greubel, Jul 01 2024
(SageMath)
@CachedFunction
def a(n): # a = A026639
if n<4: return (5*4^(n-1) - 0^(n-1))/4
else: return ((7*n^2 - 4*n + 1)*a(n-1) + 2*n*(2*n-1)*a(n-2))/(2*(n^2-1))
[a(n) for n in range(1, 41)] # G. C. Greubel, Jul 01 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved