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.
%I A206307 #17 Dec 20 2022 04:42:46
%S A206307 0,6,246,17718,1948974,304039950,63848389494,17366761942374,
%T A206307 5939432584291902,2494561685402598846,1262248212813715016070,
%U A206307 757348927688229009642006,531658947237136764768688206,431707065156555052992174823278
%N A206307 a(n) = ((2*n+2)*(2*n+3) - 1)*a(n-1) + 2*n*(2*n+1)*a(n-2), a(0)=0, a(1)=6.
%C A206307 The numerators of the fractions limiting to the value of A206530.
%D A206307 E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.
%H A206307 G. C. Greubel, <a href="/A206307/b206307.txt">Table of n, a(n) for n = 0..220</a>
%F A206307 a(n) = A125202(n+2)*a(n-1) + A002943(n)*a(n-2), a(0) = 0, a(1) = 6.
%t A206307 RecurrenceTable[{a[n]==((2n+3)(2n+2)-1)a[n-1]+2n(2n+1)a[n-2],a[0]==0,a[1]==6},a,{n,15}]
%o A206307 (Magma) [n le 2 select 6*(n-1) else (4*n^2+2*n-1)*Self(n-1) + 2*(n-1)*(2*n-1)*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Dec 20 2022
%o A206307 (SageMath)
%o A206307 @CachedFunction
%o A206307 def a(n): return 6*n if (n<2) else (4*n^2+10*n+5)*a(n-1) + 2*n*(2*n+1)*a(n-2)
%o A206307 [a(n) for n in range(31)] # _G. C. Greubel_, Dec 20 2022
%Y A206307 Cf. A002943, A125202, A206308, A206530.
%K A206307 nonn
%O A206307 0,2
%A A206307 _Seiichi Kirikami_, Feb 11 2012