

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
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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[12*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

Table of n, a(n) for n=0..77.
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^p1) = 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



