A026639 a(n) = A026637(2*n, n-1).

1, 5, 20, 74, 278, 1049, 3980, 15170, 58052, 222914, 858512, 3314960, 12829070, 49748705, 193259660, 751954250, 2929965020, 11431262390, 44651369720, 174597927740, 683388447260, 2677230376490, 10496941482680, 41188078562324

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026637, A026638, A026640, A026641, A026642, A026643, A026644.

Cf. A026645, A026646, A026647, A026966, A026967, A026968, A026969.

Cf. A026970.

Programs

Magma

[1] cat [n le 2 select 5*(3*n-2) else ((7*n^2+10*n+4)*Self(n-1) + 2*(2*n+1)*(n+1)*Self(n-2))/(2*n*(n+2)): n in [1..40]]; // G. C. Greubel, Jul 01 2024

Mathematica

a[n_]:= a[n]= If[n<4, (5*4^(n-1) -Boole[n==1])/4, ((7*n^2-4*n+1)*a[n- 1] +2*n*(2*n-1)*a[n-2])/(2*(n^2-1))];
Table[a[n], {n,40}] (* G. C. Greubel, Jul 01 2024 *)

SageMath

@CachedFunction
def a(n): # a = A026639
    if n<4: return (5*4^(n-1) - 0^(n-1))/4
    else: return ((7*n^2 - 4*n + 1)*a(n-1) + 2*n*(2*n-1)*a(n-2))/(2*(n^2-1))
[a(n) for n in range(1,41)] # G. C. Greubel, Jul 01 2024

Formula

a(n) = ((7*n^2 - 4*n + 1)*a(n-1) + 2*n*(2*n-1)*a(n-2))/(2*(n^2-1)), with a(0) = 1, a(1) = 5, a(2) = 20. - G. C. Greubel, Jul 01 2024