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 A153359 Scaled coefficients of the M. O. Rubinstein polynomials. 0
 1, -1, 1, -2, -1, 3, -2, -1, 2, 1, -152, -78, 125, 90, 15, -216, -114, 157, 135, 35, 3, -41424, -22444, 27552, 26551, 8505, 1197, 63, -66000, -36620, 40976, 42917, 15652, 2814, 252, 9, -13037952, -7390832, 7652084, 8557940, 3414775, 714840, 83790, 5220, 135, -21995904 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The polynomials alpha_{k}(s) are defined in formula (1.4) in the paper cited below. The coefficients are in ascending order. LINKS M. O. Rubinstein, Identities for the Riemann Zeta function., arXiv:0812.2592 [math.NT] FORMULA 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). EXAMPLE alpha_{0}(t) = 1 / 1; alpha_{1}(t) = (-1 + t) / 2; alpha_{2}(t) = (-2 - t + 3t^2) / 24; alpha_{3}(t) = (-2 - t + 2t^2 + t^3) / 48; MATHEMATICA 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; a53657[n_] := Product[p^Sum[Floor[(n - 1)/((p - 1) p^k)], {k, 0, n}], {p, Prime[Range[n]]}]; row[k_] := CoefficientList[alpha[k, t]*a53657[k + 1], t]; Table[row[k], {k, 0, 7}] // Flatten (* Jean-François Alcover, Jul 19 2018 *) CROSSREFS Cf. A053657. Sequence in context: A026176 A026141 A089209 * A240474 A023510 A005678 Adjacent sequences:  A153356 A153357 A153358 * A153360 A153361 A153362 KEYWORD easy,sign,tabl AUTHOR Peter Luschny, Dec 24 2008 EXTENSIONS More terms from Giovanni Resta, Jul 19 2018 STATUS approved

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Last modified August 26 01:30 EDT 2019. Contains 326324 sequences. (Running on oeis4.)