A144501 Main diagonal of array in A144502.

1, 2, 30, 1633, 198773, 42965211, 14505751627, 7051160946740, 4664901181968498, 4030793305701978223, 4407914679125170417031, 5950921219972964057360847, 9721118017169914469460646225, 18898282608956442548700379478918, 43117198379072165094561711078882078, 114089724623922992953782697056886301761

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..205

Crossrefs

Cf. A144502.

Programs

Magma

I:=[1,2,30]; [n le 3 select I[n] else ( 3*(3*n-7)*(3*n-11)*(9*n^2 - 39*n + 41)*Self(n-1) + 3*(3*n-5)*Self(n-2) - (3*n-8)*(3*n-5)*Self(n-3) )/(2*(3*n-8)*(3*n-11)): n in [1..30]]; // G. C. Greubel, Oct 09 2023

Mathematica

a[n_]:= a[n]= If[n==0, 1, If[n<3, 2*(15)^(n-1), (3*(3*n-4)*(3*n-8)*(9*n^2- 21*n+11)*a[n-1] +3*(3*n-2)*a[n-2] -(3*n-5)*(3*n-2)*a[n-3])/(2*(3*n-5)*(3*n-8))]];
Table[a[n], {n,0,30}] (* G. C. Greubel, Oct 09 2023 *)

SageMath

@CachedFunction
def a(n): # A144503
    if (n<3): return (1,2,30)[n]
    else: return ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8))
[a(n) for n in range(31)] # G. C. Greubel, Oct 09 2023

Formula

a(n) ~ 3^(3*n - 3/2) * n^(2*n - 1) / (2^(n-1) * exp(2*n - 1)). - Vaclav Kotesovec, Apr 06 2019

a(n) = ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8)), with a(0) = 1, a(1) = 2, a(3) = 30. - G. C. Greubel, Oct 09 2023