A026630 a(n) = A026626(2*n-1, n-1).

1, 4, 14, 49, 177, 650, 2417, 9071, 34289, 130360, 497928, 1909322, 7345470, 28338826, 109597727, 424761659, 1649314553, 6414825656, 24986917292, 97458970094, 380589237038, 1487882440676, 5822592097682, 22806739654454

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026626, A026627, A026628, A026629, A026631, A026632, A026633.

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

Cf. A026965.

Programs

Magma

[1] cat [n le 2 select 2*3^n -2^n else ((357*n^3 -554*n^2 -59*n +132)*Self(n-1) +2*(2*n-3)*(51*n^2 +n -14)*Self(n-2))/(2*(n+1)*(51*n^2-101*n+36)): n in [1..40]]; // G. C. Greubel, Jun 20 2024

Mathematica

a[n_]:= a[n]= If[n<4, 2*3^(n-1) -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,40}] (* G. C. Greubel, Jun 20 2024 *)

SageMath

@CachedFunction
def a(n): # a = A026630
    if (n<4): return 2*3^(n-1) -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(1,41)] # G. C. Greubel, Jun 20 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)), with a(1) = 1, a(2) = 4, and a(3) = 14. - G. C. Greubel, Jun 20 2024