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Numerator of Euler(n,2).
6

%I #15 Jan 02 2023 12:30:47

%S 1,3,2,9,2,3,2,33,2,-27,2,699,2,-5457,2,929601,2,-3202287,2,221930589,

%T 2,-4722116517,2,968383680843,2,-14717667114147,2,2093660879252679,2,

%U -86125672563201177,2,129848163681107302017,2,-868320396104950823607,2,209390615747646519456969

%N Numerator of Euler(n,2).

%H Vincenzo Librandi, <a href="/A143074/b143074.txt">Table of n, a(n) for n = 0..200</a>

%H Vladimir Shevelev, <a href="https://arxiv.org/abs/1708.08096">On a Luschny question</a>, arXiv:1708.08096 [math.NT], 2017.

%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2017-September/017929.html">A formula for numerator of Euler(n,k)</a>, Wed Sep 06 2017.

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

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

%F for n==3 (mod 4), a(n) = 2*A006519(n+1) + A002425((n+1)/2). - _Vladimir Shevelev_, Sep 04 2017

%e 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

%t Numerator[EulerE[Range[0,40],2]] (* _Vincenzo Librandi_, May 03 2012 *)

%Y For denominators see A006519.

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

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 10 2009