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%I #9 Jul 02 2024 02:15:13
%S 1,5,20,74,278,1049,3980,15170,58052,222914,858512,3314960,12829070,
%T 49748705,193259660,751954250,2929965020,11431262390,44651369720,
%U 174597927740,683388447260,2677230376490,10496941482680,41188078562324
%N a(n) = A026637(2*n, n-1).
%H G. C. Greubel, <a href="/A026639/b026639.txt">Table of n, a(n) for n = 1..1000</a>
%F 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
%t 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))];
%t Table[a[n], {n,40}] (* _G. C. Greubel_, Jul 01 2024 *)
%o (Magma)
%o [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
%o (SageMath)
%o @CachedFunction
%o def a(n): # a = A026639
%o if n<4: return (5*4^(n-1) - 0^(n-1))/4
%o else: return ((7*n^2 - 4*n + 1)*a(n-1) + 2*n*(2*n-1)*a(n-2))/(2*(n^2-1))
%o [a(n) for n in range(1,41)] # _G. C. Greubel_, Jul 01 2024
%Y Cf. A026637, A026638, A026640, A026641, A026642, A026643, A026644.
%Y Cf. A026645, A026646, A026647, A026966, A026967, A026968, A026969.
%Y Cf. A026970.
%K nonn
%O 1,2
%A _Clark Kimberling_
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