A026627 - OEIS

%I #8 Jun 19 2024 16:49:49

%S 1,3,8,28,98,354,1300,4834,18142,68578,260720,995856,3818644,14690940,

%T 56677652,219195454,849523318,3298629106,12829651312,49973834584,

%U 194917940188,761178474076,2975764881352,11645184195364

%N a(n) = A026626(2*n, n).

%H G. C. Greubel, <a href="/A026627/b026627.txt">Table of n, a(n) for n = 0..1000</a>

%F 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.

%t 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))];

%t Table[a[n], {n,0,40}] (* _G. C. Greubel_, Jun 19 2024 *)

%o (Magma)

%o [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

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A026627

%o     if n<2: return 2*n+1

%o     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))

%o [a(n) for n in range(41)] # _G. C. Greubel_, Jun 19 2024

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

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

%Y Cf. A026965.

%K nonn

%O 0,2

%A _Clark Kimberling_