0,1

Denominator of Zeta'[ -2n].

For n>=0, a(n) = 2 * A001316(n) [From N. J. A. Sloane, May 30 2009]

For n>0, a(n) = 4 * A048896(n) [From Peter Luschny (peter(AT)luschny.de), May 02 2009]

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

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 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.

Eric Weisstein's World of Mathematics, Riemann Zeta Function

a(0) = 2; for n>0, write n = 2^i + j where 0 <= j < 2^i; then a(n) = 2*a(j).

-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), ...

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); [From Peter Luschny (peter(AT)luschny.de), May 02 2009]

Denominator[(2*n)!/2^(2*n + 1)]

Cf. A001316, A117972, A160464, A094665, A160468.

Sequence in context: A011173 A162943 A131136 this_sequence A140434 A107748 A005884

Adjacent sequences: A117970 A117971 A117972 this_sequence A117974 A117975 A117976

nonn,frac

Eric Weisstein (eric(AT)weisstein.com), Apr 06, 2006

First term added, offset changed and edited by Johannes W. Meijer (meijgia(AT)hotmail.com), May 15 2009. Further edits, May 20 2009, Jun 02 2009.

Entry revised by N. J. A. Sloane, May 30 2009