0,2

The first difference with sequence A009843 (expansion of x/cos(x)) occurs at a(10). An explanation can be found in the 'look-a-like' of the numerators of (2*n+1)/(4^(2*n+1)-2^(2*n+1)) with the odd numbers 2n+1 (cf. A160144).

A156769 describes a similar 'look-a-like' with A036279 (expansion of tan(x)).

a := n -> (-1)^iquo(n, 2)*euler(n)*(n+1)/(4^(n+1)-2^(n+1));

seq(numer(a(2*n)), n=0..13);

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

Sequence in context: A132617 A143925 A074708 this_sequence A009843 A136173 A003024

Adjacent sequences: A160140 A160141 A160142 this_sequence A160144 A160145 A160146

frac,nonn

Peter Luschny (peter(AT)luschny.de), May 03 2009