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 A117973 a(n) = 2^(wt(n)+1), where wt() = A000120(). 7
 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 128, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Denominator of Zeta'(-2n). If Gould's sequence A001316 is written as a triangle, this is what the rows converge to. In other words, let S_0 = [2], and construct S_{n+1} by following S_n with 2*S_n. Then this is S_{oo}. - N. J. A. Sloane, May 30 2009 In A160464 the coefficients of the ES1 matrix are defined. This matrix led to the discovery that the successive differences of the ES1[1-2*m,n] coefficients for m = 1, 2, 3, ..., are equal to the values of Zeta'(-2n), see also A094665 and A160468. - Johannes W. Meijer, May 24 2009 LINKS J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function FORMULA For n>=0, a(n) = 2 * A001316(n). - N. J. A. Sloane, May 30 2009 For n>0, a(n) = 4 * A048896(n). - Peter Luschny, May 02 2009 a(0) = 2; for n>0, write n = 2^i + j where 0 <= j < 2^i; then a(n) = 2*a(j). a((2*n+1)*2^p-1) = 2^(p+1) * A001316(n), p >= 0. - Johannes W. Meijer, Jan 28 2013 EXAMPLE -zeta(3)/(4*Pi^2), (3*zeta(5))/(4*Pi^4), (-45*zeta(7))/(8*Pi^6), (315*zeta(9))/(4*Pi^8), (-14175*zeta(11))/(8*Pi^10), ... MAPLE S := [2]; S := [op(S), op(2*S)]; # repeat ad infinitum! - N. J. A. Sloane, May 30 2009 a := n -> 2^(add(i, i=convert(n, base, 2))+1); # Peter Luschny, May 02 2009 MATHEMATICA Denominator[(2*n)!/2^(2*n + 1)] CROSSREFS Cf. A001316, A117972, A160464, A094665, A160468, A220466. Sequence in context: A011173 A162943 A131136 * A140434 A107748 A005884 Adjacent sequences:  A117970 A117971 A117972 * A117974 A117975 A117976 KEYWORD nonn,frac AUTHOR Eric W. Weisstein, Apr 06 2006 EXTENSIONS Entry revised by N. J. A. Sloane, May 30 2009 STATUS approved

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Last modified May 25 01:17 EDT 2019. Contains 323534 sequences. (Running on oeis4.)