A026642 - OEIS

%I #11 Jul 02 2024 02:17:20

%S 1,7,28,112,439,1711,6652,25846,100450,390670,1520764,5925718,

%T 23112931,90239407,352654084,1379410438,5400188206,21157958962,

%U 82959736504,325514137048,1278093308806,5021436970822,19740128055928

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

%H G. C. Greubel, <a href="/A026642/b026642.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = ( (7*n^2 - 11*n + 6)*a(n-1) + 2*(n-1)*(2*n-1)*a(n-2) )/(2*(n-2)*(n+1)), n >= 4. - _G. C. Greubel_, Jul 01 2024

%t a[n_]:= a[n]= If[n<4, 7^(n-2), ((7*n^2-11*n+6)*a[n-1] + 2*(n-1)*(2*n- 1)*a[n-2])/(2*(n-2)*(n+1))];

%t Table[a[n], {n,2,40}] (* _G. C. Greubel_, Jul 01 2024 *)

%o (Magma)

%o [n le 2 select 7^(n-1) else ((7*n^2+3*n+2)*Self(n-1) + 2*n*(2*n+1)*Self(n-2))/(2*(n-1)*(n+2)): n in [1..40]]; // _G. C. Greubel_, Jul 01 2024

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A026642

%o     if n<4: return 7^(n-2)

%o     else: return ((7*n^2-11*n+6)*a(n-1) + 2*(n-1)*(2*n-1)*a(n-2))/(2*(n-2)*(n+1))

%o [a(n) for n in range(2,41)] # _G. C. Greubel_, Jul 01 2024

%Y Cf. A026637, A026638, A026639, A026640, A026641, A026643, A026644.

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

%Y Cf. A026970.

%K nonn

%O 2,2

%A _Clark Kimberling_