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%I #8 Jul 19 2018 08:15:35
%S 1,-1,1,-2,-1,3,-2,-1,2,1,-152,-78,125,90,15,-216,-114,157,135,35,3,
%T -41424,-22444,27552,26551,8505,1197,63,-66000,-36620,40976,42917,
%U 15652,2814,252,9,-13037952,-7390832,7652084,8557940,3414775,714840,83790,5220,135,-21995904
%N Scaled coefficients of the M. O. Rubinstein polynomials.
%C The polynomials alpha_{k}(s) are defined in formula (1.4) in the paper cited below. The coefficients are in ascending order.
%H M. O. Rubinstein, <a href="http://arxiv.org/abs/0812.2592">Identities for the Riemann Zeta function.</a>, arXiv:0812.2592 [math.NT]
%F The coefficients of the polynomials alpha_{k}(s)*A053657(k) where alpha_{0}(s) = 1 and alpha_{k+1}(s) = (s-1)/(k+2)-sum(j=1..k,((j-(s-1)*(k-j+1))/(k-j+2))*alpha_{j}(s))/(k+1).
%e alpha_{0}(t) = 1 / 1;
%e alpha_{1}(t) = (-1 + t) / 2;
%e alpha_{2}(t) = (-2 - t + 3t^2) / 24;
%e alpha_{3}(t) = (-2 - t + 2t^2 + t^3) / 48;
%t alpha[0, _] = 1; alpha[k_, s_] := (s - 1)/(k + 1) - Sum[((j - (s - 1)*(k - j))/(k - j + 1))*alpha[j, s]/(k), {j, 1, k - 1}] // Expand;
%t a53657[n_] := Product[p^Sum[Floor[(n - 1)/((p - 1) p^k)], {k, 0, n}], {p, Prime[Range[n]]}];
%t row[k_] := CoefficientList[alpha[k, t]*a53657[k + 1], t];
%t Table[row[k], {k, 0, 7}] // Flatten (* _Jean-François Alcover_, Jul 19 2018 *)
%Y Cf. A053657.
%K easy,sign,tabl
%O 0,4
%A _Peter Luschny_, Dec 24 2008
%E More terms from _Giovanni Resta_, Jul 19 2018
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