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%I #29 Feb 06 2022 02:09:59
%S 1,4,40,3280,21523360,926510094425920,1716841910146256242328924544640,
%T 5895092288869291585760436430706259332839105796137920554548480
%N a(n) = (3^(2^n)-1)/2.
%C Denominator of b(n) where b(n) = 1/2*(b(n-1) + 1/b(n-1)), b(0)=2. - _Vladeta Jovovic_, Aug 15 2002
%H Harry J. Smith, <a href="/A059918/b059918.txt">Table of n, a(n) for n = 0..11</a>
%F a(n) = a(n-1)*(3^(2^(n-1))+1) with a(0) = 1.
%F a(n) = (3^(2^n)-1)/2 = (A059723(n+1)-A059723(n))/A059723(n) = A059917(n)-1 = a(n-1)*A059919(n-1) = a(n-1)*(A011764(n-1)+1)
%F 1 = Sum_{n>=0} 3^(2^n)/a(n+1). 1 = 3/4 + 9/40 + 81/3280 + 6561/21523360 + ...; with partial sums: 3/4, 39/40, 3279/3280, 21523359/21523360, ..., (a(n)-1)/a(n), ... . - _Gary W. Adamson_, Jun 22 2003
%F A136308(n) = A007089(a(n)). - _Jason Kimberley_, Dec 19 2012
%t Array[(3^(2^#) - 1)/2 &, 8, 0] (* _Michael De Vlieger_, Feb 05 2022 *)
%o (PARI) { for (n=0, 11, write("b059918.txt", n, " ", (3^(2^n) - 1)/2); ) } \\ _Harry J. Smith_, Jun 30 2009
%Y Cf. A059917 (numerators).
%Y Cf. A059723, A059917, A059919, A011764.
%Y Cf. A007089, A136308.
%K nonn,easy
%O 0,2
%A _Henry Bottomley_, Feb 08 2001
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