A117973 a(n) = 2^(wt(n)+1), where wt() = A000120().

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

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

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^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 * A347191 A337256 A140434

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