A144500 Column 4 of array in A144502.

1, 65, 946, 13219, 198773, 3289726, 60042295, 1203809111, 26367604594, 627370195033, 16127774194871, 445733080387750, 13185075339881521, 415765494276887249, 13925084982848794378, 493754789222478044011, 18480155500259244528605, 728143711886491334229526

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 13 2008

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..401

Crossrefs

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

Programs

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

Mathematica

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)];
Table[a[n], {n,0,40}] (* G. C. Greubel, Oct 08 2023 *)

SageMath

@CachedFunction
def a(n): # a = A144500
    if (n<2): return (65)^n
    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)
[a(n) for n in range(41)] # G. C. Greubel, Oct 08 2023

Formula

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