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Coefficients a(n) of a series connected with the odd primes.
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%I #7 Mar 30 2012 17:26:02

%S 1,-1,-1,0,0,2,1,0,-2,-5,2,3,5,6,-10,-12,-9,11,32,11,-5,-55,-61,29,84,

%T 129,9,-188,-232,-136,322,567,255,-354,-1185,-840,585,2038,2318,-594,

%U -3909,-4761,-929,7387,10441,3930,-11137,-23097,-12215,16547,44716,36786,-23108

%N Coefficients a(n) of a series connected with the odd primes.

%C The series reciprocal to the series with coefficients in A005097 has (integer) coefficients with irregular signs and values. In contrast the series reciprocal to the series with coefficients = primes themselves has coefficients (A030018) with alternating signs and regular growth. The radius of convergence (defined from consecutive coefficients ratio) of that series is 0.686777834460.

%F Sum(a(i)*x^(i-1), (i=1, inf))=1/(1+sum(1/2(p(i)-1)*x^(i-1), i=2, inf)) =1/(1+sum( A005097(i)*x^(i), i=1, inf))

%Y Cf. A005097, A030018.

%K easy,sign

%O 1,6

%A _Zak Seidov_, Sep 16 2002