A171078 Numerator of s_{2n}, where s_0 = 1, s_n = | 2^n*(2^(n-1)-1)*Bernoulli(n)/n! | for n>0.

1, 1, 7, 62, 127, 146, 2828954, 32764, 16931177, 11499383114, 183092554714, 13299018868, 3965530936622474, 88306001369044, 260212136880609068, 7400951287808330864888, 16555640865486520478399, 16179883156293315362, 58334570685127434999731256122

Offset

0,3

References

F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer, 3rd. ed., 1966; p. 12, Eq. 11.

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: (x*sec(x)^2/tan(x))/2=sum{n>=0, a(n)*x^(2*n)} - Vladimir Kruchinin, Feb 04 2013

a(n) = numerator(Zeta(2*n)*(4^n-2)/Pi^(2*n)). - Peter Luschny, Aug 11 2014

Example

1, 1/3, 7/45, 62/945, 127/4725, 146/13365, 2828954/638512875, 32764/18243225, 16931177/23260111875, 11499383114/38979295480125, ...

Maple

A171078 := n -> numer(Zeta(2*n)*(4^n-2)/Pi^(2*n));
seq(A171078(n), n=0..18); # Peter Luschny, Aug 11 2014

Crossrefs

Cf. A171079 (denominators).

Sequence in context: A145507 A254121 A047685 * A368057 A180776 A353099

Adjacent sequences: A171075 A171076 A171077 * A171079 A171080 A171081

Keyword

nonn,frac

Author

N. J. A. Sloane, Sep 06 2010

Status

approved