A143074 Numerator of Euler(n,2).

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

Offset: 0

Author

N. J. A. Sloane, Nov 10 2009

Keywords

• sign
• frac

Examples

			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
		

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.

Crossrefs

For denominators see A006519.

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

Programs

Mathematica

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

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