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A171078 Numerator of s_{2n}, where s_0 = 1, s_n = | 2^n*(2^(n-1)-1)*Bernoulli(n)/n! | for n>0. 2
1, 1, 7, 62, 127, 146, 2828954, 32764, 16931177, 11499383114, 183092554714, 13299018868, 3965530936622474, 88306001369044, 260212136880609068, 7400951287808330864888, 16555640865486520478399, 16179883156293315362, 58334570685127434999731256122 (list; graph; refs; listen; history; text; internal format)
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 * A180776 A024089 A327588

Adjacent sequences:  A171075 A171076 A171077 * A171079 A171080 A171081

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Sep 06 2010

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)