cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A026630 a(n) = A026626(2*n-1, n-1).

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%I A026630 #8 Jun 20 2024 16:29:00
%S A026630 1,4,14,49,177,650,2417,9071,34289,130360,497928,1909322,7345470,
%T A026630 28338826,109597727,424761659,1649314553,6414825656,24986917292,
%U A026630 97458970094,380589237038,1487882440676,5822592097682,22806739654454
%N A026630 a(n) = A026626(2*n-1, n-1).
%H A026630 G. C. Greubel, <a href="/A026630/b026630.txt">Table of n, a(n) for n = 1..1000</a>
%F A026630 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)), with a(1) = 1, a(2) = 4, and a(3) = 14. - _G. C. Greubel_, Jun 20 2024
%t A026630 a[n_]:= a[n]= If[n<4, 2*3^(n-1) -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 A026630 Table[a[n], {n,40}] (* _G. C. Greubel_, Jun 20 2024 *)
%o A026630 (Magma)
%o A026630 [1] cat [n le 2 select 2*3^n -2^n else ((357*n^3 -554*n^2 -59*n +132)*Self(n-1) +2*(2*n-3)*(51*n^2 +n -14)*Self(n-2))/(2*(n+1)*(51*n^2-101*n+36)): n in [1..40]]; // _G. C. Greubel_, Jun 20 2024
%o A026630 (SageMath)
%o A026630 @CachedFunction
%o A026630 def a(n): # a = A026630
%o A026630     if (n<4): return 2*3^(n-1) -2^(n-1)
%o A026630     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 A026630 [a(n) for n in range(1,41)] # _G. C. Greubel_, Jun 20 2024
%Y A026630 Cf. A026626, A026627, A026628, A026629, A026631, A026632, A026633.
%Y A026630 Cf. A026634, A026635, A026636, A026961, A026962, A026963, A026964.
%Y A026630 Cf. A026965.
%K A026630 nonn
%O A026630 1,2
%A A026630 _Clark Kimberling_