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%I #12 Mar 05 2022 04:16:11
%S 1,0,1,1,11,12,107,119,10579,42435,53014,95449,721157,15960903,
%T 16682060,49325023,164657129,4330410377,4495067506,53776152943,
%U 58271220449,636488357433,694759577882,6889324558371,21362733252995
%N Denominators of the convergents of the continued fraction for Catalan's constant L(2, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4.
%F chi4(k) = Kronecker(-4, k); chi4(k) is 0, 1, 0, -1 when k reduced modulo 4 is 0, 1, 2, 3, respectively; chi4 is A101455.
%F Series: L(2, chi4) = Sum_{k>=1} chi4(k) k^{-2} = 1 - 1/3^2 + 1/5^2 - 1/7^2 + 1/9^2 - 1/11^2 + 1/13^2 - 1/15^2 + ...
%e L(2, chi4) = 0.91596559417721901505460351493238411... = [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 10/11, 1/12, 98/107, 109/119, 9690/10579, 38869/42435, 48559/53014, 87428/95449, 660555/721157, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.
%t nmax = 100; cfrac = ContinuedFraction[Catalan, nmax + 1]; Join[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
%Y Cf. A006752, A014538, A054543, A104338, A118323, A153069 (numerators).
%K nonn,frac,easy
%O -2,5
%A _Stuart Clary_, Dec 17 2008
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