A093596 a(n) = Pi^(2n)*denominator of Sum_{k in A030059} 1/k^(2n).

2, 2, 691, 7234, 174611, 163327586881, 13571120588, 55769228412163778, 1154372017217796891921391, 45587914559383477650447161, 786244320265033260236106076, 1325861528365506758393998232189714777, 162188234491877244039346965481488044, 4806877204106337185378935774268985038351236

Offset: 1

Author

Eric W. Weisstein, Apr 03 2004

Keywords

• nonn
• easy
• frac

Examples

			9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...
		

Links

• Eric Weisstein's World of Mathematics, Prime Sums.

Crossrefs

Cf. A030059, A093595 (numerators).

Programs

Mathematica

Table[Denominator[(Zeta[2*n]^2 - Zeta[4*n]) / (2*Zeta[2*n]*Zeta[4*n])] / Pi^(2*n), {n, 1, 12}] (* Amiram Eldar, Jan 19 2025 *)

Formula

a(n) = denominator((zeta(2n)^2-zeta(4n))/(2*zeta(2n)*zeta(4n)))/Pi^(2n). See Eqns (28) to (31) of the link.