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

0,2

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A027463 A305264 A279639 * A086021 A168029 A219413

Adjacent sequences: A144497 A144498 A144499 * A144501 A144502 A144503

Keyword

nonn

Author

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

Status

approved