A053005 Denominator of beta(2n+1)/Pi^(2n+1), where beta(m) = Sum_{k=0..inf} (-1)^k/(2k+1)^m.

4, 32, 1536, 184320, 8257536, 14863564800, 1569592442880, 5713316492083200, 1096956766479974400, 6713375410857443328000, 408173224980132554342400, 18857602994082124010618880000, 640578267860512766391484416000

Offset

0,1

References

J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 384, Problem 15.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Problem 37, beta(n).

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Dirichlet Beta Function

Example

beta(5) = 5*Pi^5/1536 so a(2)=1536.

Mathematica

beta[1] = Pi/4; beta[m_] := (Zeta[m, 1/4] - Zeta[m, 3/4])/4^m; a[n_, p_] := a[n, p] = beta[2*n+1]/Pi^(2*n+1) // N[#, p]& // Rationalize[#, 0]& // Denominator; a[n_] := Module[{p = 16}, a[n, p]; p = 2*p; While[a[n, p] != a[n, p/2], p = 2*p]; a[n, p]]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Aug 19 2013 *)

Crossrefs

Cf. A046976.

Sequence in context: A231991 A028369 A081790 * A257583 A258122 A012092

Adjacent sequences: A053002 A053003 A053004 * A053006 A053007 A053008

Keyword

nonn,frac,nice,easy

Author

N. J. A. Sloane, Feb 21 2000

Status

approved