A026631 a(n) = A026626(2*n-1, n-2).

1, 7, 30, 119, 467, 1820, 7076, 27493, 106848, 415538, 1617504, 6302416, 24581249, 95968478, 375029576, 1466881997, 5742440324, 22498218218, 88212326756, 346114729562, 1358944775654, 5338963361408, 20987909276600

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Formula

a(n) = ((357*n^4 -1982*n^3 +3819*n^2 -3082*n +840)*a(n-1) +2*(2*n-5)*(51*n^3 -152*n^2 +133*n -24)*a(n-2))/(2*(n+1)*(51*n^3 -305*n^2 +590*n -360)), for n >= 5, with a(2) = 1, a(3) = 7, and a(4) = 30. - G. C. Greubel, Jun 20 2024

Mathematica

a[n_]:= a[n]= If[n<5, 23*n-62, ((357*n^4 -1982*n^3 +3819*n^2 -3082*n + 840)*a[n-1] +2*(2*n-5)*(51*n^3 -152*n^2 +133*n -24)*a[n-2] )/(2*(n + 1)*(51*n^3 -305*n^2 +590*n -360))] +17*Boole[n==2];
Table[a[n], {n, 2, 40}] (* G. C. Greubel, Jun 20 2024 *)

Prog

(Magma)
[1] cat [n le 2 select 23*(n+2)-62 else ((357*n^4 +874*n^3 +495*n^2 - 166*n -192)*Self(n-1) + 2*(2*n-1)*(51*n^3 +154*n^2 +137*n + 42 )*Self(n-2))/(2*(n+3)*(51*n^3 +n^2 -18*n +8)): n in [1..40]]; // G. C. Greubel, Jun 20 2024
(SageMath)
@CachedFunction
def a(n): # a = A026631
    if (n==2): return 1
    elif (n<5): return 23*n - 62
    else: return ((357*n^4 -1982*n^3 +3819*n^2 -3082*n +840)*a(n-1) +2*(2*n-5)*(51*n^3 -152*n^2 +133*n -24)*a(n-2))/(2*(n+1)*(51*n^3 -305*n^2 +590*n -360))
[a(n) for n in range(2, 41)] # G. C. Greubel, Jun 20 2024

Crossrefs

Cf. A026626, A026627, A026628, A026629, A026630, A026632, A026633.

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

Cf. A026965.

Sequence in context: A375995 A269084 A055269 * A037709 A378502 A037611

Adjacent sequences: A026628 A026629 A026630 * A026632 A026633 A026634

Keyword

nonn

Author

Clark Kimberling

Status

approved