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A206532 a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.

%I A206532 #13 Sep 16 2018 09:06:21
%S A206532 1,11,331,18535,1668151,220195931,40075659443,9618158266319,
%T A206532 2943156429493615,1118399443207573699,516700542761899048939,
%U A206532 285218699604568275014327,185392154742969378759312551,140156468985684850342040288555
%N A206532 a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.
%C A206532 The denominators of the fractions limiting to the value of A206533.
%D A206532 E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc.,1966.
%H A206532 Robert Israel, <a href="/A206532/b206532.txt">Table of n, a(n) for n = 0..223</a>
%F A206532 a(n) = A082108*a(n-1) + A002939*a(n-2), a(0) = 1, a(1) = 11.
%F A206532 a(n) = -4*n*(-1)^n*(n+1)*LommelS1(2*n+1/2, 3/2, 1)-2*(-1)^n*(n+1)*LommelS1(2*n+3/2, 1/2, 1)+(1-cos(1))*(2*n+2)!+(-1)^n. - _Robert Israel_, Sep 16 2018
%p A206532 f:= gfun:-rectoproc({a(n) = (2*(n+1)*(2*n+1)-1) * a(n-1) + 2*n*(2*n-1) * a(n-2), a(0) = 1, a(1) = 11},a(n),remember):
%p A206532 map(f, [$0..40]); # _Robert Israel_, Sep 16 2018
%t A206532 RecurrenceTable[{a[n]==(2(n+1)(2n+1)-1)a[n-1]+2n(2n-1)a[n-2],a[0]==1,a[1]==11},a,{n,15}]
%Y A206532 Cf. A002939, A082108, A206531, A206533.
%K A206532 nonn
%O A206532 0,2
%A A206532 _Seiichi Kirikami_, Feb 11 2012