A160143 a(n) = Numerator((-1)^n*Euler(2*n)*(2*n+1)/(4^(2*n+1)-2^(2*n+1))), where Euler(n) = A122045(n).

1, 3, 25, 427, 12465, 555731, 35135945, 2990414715, 329655706465, 45692713833379, 1111113564712575, 1595024111042171723, 387863354088927172625, 110350957750914345093747

Offset: 0

Author

Peter Luschny, May 03 2009

Keywords

• frac
• nonn

Comments

Resembles the coefficients of the series for x/cos(x).

The first difference with sequence A009843 (expansion of x/cos(x)) occurs at a(10). An explanation can be found in the similarity of the numerators of (2*n+1)/(2^(2*n+1)-1) and the odd numbers 2n+1 (cf. A160144).

Similarly, A156769 resembles A036279 (from the expansion of tan(x)).

Crossrefs

Cf. A009843, A122045, A160144, A160145, A036279, A156769.

Programs

Maple

a := n -> (-1)^iquo(n,2)*euler(n)*(n+1)/(4^(n+1)-2^(n+1));
seq(numer(a(2*n)),n=0..13);