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A225128
Numerators of the convolutory inverse of the primes of the form 4m+3.
2
1, -7, 16, -52, 412, -2068, 6964, -19960, 81880, -396844, 1448908, -3853348, 9668860, -45544768, 238303744, -764868256, 1962327904, -9820441204, 62744531956, -306405293056, 1228176071080, -5276516025688, 26307346186816, -126143746044604, 534479888324932
OFFSET
1,2
COMMENTS
Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (3,7,11,19,23,31,...) of primes congruent to 3 mod 4. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) -> -1.370819405....
LINKS
EXAMPLE
(3,7,11,19,23,...)**(1/3, -7/9, 16/27, -52/81, 412/243,...) = (1,0,0,0,0,...), where ** denotes convolution.
MATHEMATICA
q = {}; Do[If[PrimeQ[p = 4*n + 3], 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]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Apr 29 2013
STATUS
approved