A144501 Main diagonal of array in A144502.

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

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..205

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A144502.

Sequence in context: A262004 A132104 A208093 * A198861 A162841 A158260

Adjacent sequences: A144498 A144499 A144500 * A144502 A144503 A144504

Keyword

nonn

Author

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

Status

approved