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%I #14 Dec 22 2022 02:11:52
%S 0,2,58,3250,292498,38609738,7026972314,1686473355362,516060846740770,
%T 196103121761492602,90599642253809582122,50011002524102889331346,
%U 32507151640666878065374898,24575406640344159817423422890
%N a(n) = (2*(n+1)*(2*n+1)-1)*a(n-1) + 2*n*(2*n-1)*a(n-2), a(0)=0, a(1)=2.
%C The numerators of the fractions limiting to the value of A206533.
%D E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.
%H G. C. Greubel, <a href="/A206531/b206531.txt">Table of n, a(n) for n = 0..220</a>
%F a(n) = A082108(n)*a(n-1) + A002939(n)*a(n-2), a(0) = 0, a(1) = 2.
%t RecurrenceTable[{a[n]==(2(n+1)(2n+1)-1)a[n-1]+2n(2n-1)a[n-2],a[0]==0,a[1]==2},a,{n,15}]
%o (Magma) [n le 2 select 2*(n-1) else (2*n*(2*n-1)-1)*Self(n-1) + 2*(n-1)*(2*n-3)*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Dec 21 2022
%o (SageMath)
%o @CachedFunction
%o def a(n): # a = A206531
%o if (n<2): return 2*n
%o else: return (2*(n+1)*(2*n+1)-1)*a(n-1) + 2*n*(2*n-1)*a(n-2)
%o [a(n) for n in range(31)] # _G. C. Greubel_, Dec 21 2022
%Y Cf. A002939, A082108, A206532, A206533.
%K nonn
%O 0,2
%A _Seiichi Kirikami_, Feb 11 2012
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