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%I #5 Apr 30 2013 12:11:25
%S 1,-13,84,-712,6916,-55788,432584,-3555212,28927916,-229458788,
%T 1847086584,-14858027212,118242773916,-945499611788,7556178053084,
%U -60048635124212,477995366994916,-3810212526827288,30296614848644584,-240796293647346212,1916211884628153416
%N Numerators of the convolutory inverse of the primes of the form 4m+1.
%C Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (5,13,17,29,37,...) of primes congruent to 1 mod 4. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) -> -1.59045463062282....
%H Clark Kimberling, <a href="/A225129/b225129.txt">Table of n, a(n) for n = 1..1000</a>
%e (5,13,17,29,37,...)**(1/5, -13/25, 84/125, -712/625, 6916/3125,...) = (1,0,0,0,0,...), where ** denotes convolution.
%t q = {}; Do[If[PrimeQ[p = 4*n + 1], AppendTo[q, p]], {n, 0, 15000}]; r[n_] := q[[n]]; k[n_] := k[n] = 0; k[1] = 1; s[n_] := s[n] = (k[n] - Sum[r[k]*s[n - k + 1], {k, 2, n}])/r[1]; t = Table[s[n], {n, 1, 40}]; Numerator[t]
%Y Cf. A030018, A225127, A225128.
%K sign,easy
%O 1,2
%A _Clark Kimberling_, Apr 29 2013
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