%I #12 Oct 08 2023 04:42:31

%S 1,65,946,13219,198773,3289726,60042295,1203809111,26367604594,

%T 627370195033,16127774194871,445733080387750,13185075339881521,

%U 415765494276887249,13925084982848794378,493754789222478044011,18480155500259244528605,728143711886491334229526

%N Column 4 of array in A144502.

%H Seiichi Manyama, <a href="/A144500/b144500.txt">Table of n, a(n) for n = 0..401</a>

%F a(n) = ((24*n^3 + 60*n^2 + 50*n + 5)*a(n-1) + (12*n^2 + 24*n + 1)*a(n-2))/(12*n^2 - 11), with a(0) = 1, a(1) = 65. - _G. C. Greubel_, Oct 08 2023

%t a[n_]:= a[n]= If[n<2, (65)^n, ((24*n^3+60*n^2+50*n+5)*a[n-1] +(12*n^2 + 24*n+1)*a[n-2])/(12*n^2-11)];

%t Table[a[n], {n,0,40}] (* _G. C. Greubel_, Oct 08 2023 *)

%o (Magma) [n le 2 select (65)^(n-1) else ((24*n^3-12*n^2+2*n-9)*Self(n-1) + (12*n^2-11)*Self(n-2))/(12*(n-1)^2 -11): n in [1..40]]; // _G. C. Greubel_, Oct 08 2023

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A144500

%o if (n<2): return (65)^n

%o else: return ((24*n^3 + 60*n^2 + 50*n + 5)*a(n-1) + (12*n^2 + 24*n + 1)*a(n-2))/(12*n^2 - 11)

%o [a(n) for n in range(41)] # _G. C. Greubel_, Oct 08 2023

%Y Cf. A144495, A144496, A144497, A144498, A144499, A144501, A144502, A144503.

%K nonn

%O 0,2

%A _David Applegate_ and _N. J. A. Sloane_, Dec 13 2008