A026628 a(n) = A026626(2*n, n-1).

1, 6, 21, 79, 296, 1117, 4237, 16147, 61782, 237208, 913466, 3526826, 13647886, 52920075, 205566205, 799791235, 3116196550, 12157265980, 47485135510, 185671296850, 726703966600, 2846827216330, 11161555459090, 43794648931054

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A026626, A026627, A026629, A026630, A026631, A026632, A026633.

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

Cf. A026965.

Programs

Magma

[n le 2 select 5*n-4 else ((357*n^4-1625*n^3+2157*n^2-841*n+60)*Self(n-1) +2*(2*n-5)*(51*n^3-101*n^2+34*n+6)*Self(n-2))/(2*(n+1)*(51*n^3-254*n^2+389*n-180)): n in [1..41]]; // G. C. Greubel, Jun 19 2024

Mathematica

a[n_]:= a[n]= If[n<3, 5*n-4, ((357*n^4 -1625*n^3 +2157*n^2 -841*n +60 )*a[n-1] +2*(2*n-5)*(51*n^3 -101*n^2 +34*n +6)*a[n-2])/(2*(n+1)*(51*n^3 -254*n^2 +389*n -180))];
Table[a[n], {n,41}]

SageMath

@CachedFunction
def a(n): # a = A026628
    if n<3: return 5*n-4
    else: return ((357*n^4 -1625*n^3 +2157*n^2 -841*n +60)*a(n-1) +2*(2*n-5)*(51*n^3 -101*n^2 +34*n +6)*a(n-2))/(2*(n+1)*(51*n^3-254*n^2+389*n-180))
[a(n) for n in range(1,41)] # G. C. Greubel, Jun 19 2024

Formula

a(n) = ( (357*n^4 - 1625*n^3 + 2157*n^2 - 841*n + 60)*a(n-1) + 2*(2*n-5)*(51*n^3 - 101*n^2 + 34*n + 6)*a(n-2) )/(2*(n+1)*(51*n^3 - 254*n^2 + 389*n - 180)), for n >= 3, with a(1) = 1, a(2) = 6. - G. C. Greubel, Jun 19 2024

a(n) ~ 17 * 2^(2*n-2) / (3*sqrt(Pi*n)). - Vaclav Kotesovec, Aug 09 2025