login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143074 Numerator of Euler(n,2). 6
1, 3, 2, 9, 2, 3, 2, 33, 2, -27, 2, 699, 2, -5457, 2, 929601, 2, -3202287, 2, 221930589, 2, -4722116517, 2, 968383680843, 2, -14717667114147, 2, 2093660879252679, 2, -86125672563201177, 2, 129848163681107302017, 2, -868320396104950823607, 2, 209390615747646519456969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Vladimir Shevelev, On a Luschny question, arXiv:1708.08096 [math.NT], 2017.

Vladimir Shevelev, A formula for numerator of Euler(n,k), Wed Sep 06 2017.

FORMULA

For even n, a(n) = 2 - delta(n,0), where delta is the Kronecker symbol;

for n==1 (mod 4), a(n) = 2*A006519(n+1) - A002425((n+1)/2);

for n==3 (mod 4), a(n) = 2*A006519(n+1) + A002425((n+1)/2). - Vladimir Shevelev, Sep 04 2017

EXAMPLE

By the formula, we have a(1) = 2*2 - 1 = 3, a(3) = 2*4 + 1 = 9, a(5) = 2*2 - 1 = 3, a(7) = 2*8 + 17 = 33, a(9) = 2*2 - 31 = -27, etc. - Vladimir Shevelev, Sep 04 2017

MATHEMATICA

Numerator[EulerE[Range[0, 40], 2]] (* Vincenzo Librandi, May 03 2012 *)

CROSSREFS

For denominators see A006519.

Cf. A002425, A157805, A157808, A157812, A157827, A157835, A157856, A157864, A157875, A157886, A157907.

Sequence in context: A272491 A010271 A291777 * A173624 A182023 A228936

Adjacent sequences:  A143071 A143072 A143073 * A143075 A143076 A143077

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 10 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 12:34 EDT 2019. Contains 322209 sequences. (Running on oeis4.)