OFFSET
1,2
COMMENTS
Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (7,13,19,31,37,...) of primes congruent to 1 mod 6. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) diverges.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
(7,13,19,31,37,...)**(1/7, -13/49, 36/343, -258/2401, 5622/16807,...) = (1,0,0,0,0,...), where ** denotes convolution.
MATHEMATICA
q = {}; Do[If[PrimeQ[p = 6*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]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Apr 29 2013
STATUS
approved