A026627 a(n) = A026626(2*n, n).

1, 3, 8, 28, 98, 354, 1300, 4834, 18142, 68578, 260720, 995856, 3818644, 14690940, 56677652, 219195454, 849523318, 3298629106, 12829651312, 49973834584, 194917940188, 761178474076, 2975764881352, 11645184195364

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026626, A026628, A026629, A026630, A026631, A026632, A026633.

Cf. A026634, A026635, A026636, A026961, A026962, A026963, A026964.

Cf. A026965.

Programs

Magma

[n le 2 select 2*n-1 else ((357*n^3-2696*n^2+6441*n-4822)*Self(n-1) +2*(2*n-7)*(51*n^2-203*n+188)*Self(n-2))/(2*(n-1)*(51*n^2-305*n+442)): n in [1..41]]; // G. C. Greubel, Jun 19 2024

Mathematica

a[n_]:= a[n]= If[n<2, 2*n+1, ((357*n^3 -1625*n^2 +2120*n -720)*a[n-1] +2*(2*n-5)*(51*n^2 -101*n +36)*a[n-2])/(2*n*(51*n^2-203*n+188))];
Table[a[n], {n,0,40}] (* G. C. Greubel, Jun 19 2024 *)

SageMath

@CachedFunction
def a(n): # a = A026627
    if n<2: return 2*n+1
    else: return ((357*n^3 -1625*n^2 +2120*n -720)*a(n-1) +2*(2*n-5)*(51*n^2 -101*n +36)*a(n-2))/(2*n*(51*n^2 -203*n +188))
[a(n) for n in range(41)] # G. C. Greubel, Jun 19 2024

Formula

a(n) = ( (357*n^3 - 1625*n^2 + 2120*n - 720)*a(n-1) + 2*(2*n-5)*(51*n^2 - 101*n + 36)*a(n-2) )/(2*n*(51*n^2 - 203*n + 188)), for n >= 2, with a(0) = 1, a(1) = 3.