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%I #16 Mar 18 2021 06:56:40
%S 1,3,25,427,12465,555731,35135945,2990414715,329655706465,
%T 45692713833379,1111113564712575,1595024111042171723,
%U 387863354088927172625,110350957750914345093747
%N a(n) = Numerator((-1)^n*Euler(2*n)*(2*n+1)/(4^(2*n+1)-2^(2*n+1))), where Euler(n) = A122045(n).
%C Resembles the coefficients of the series for x/cos(x).
%C 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).
%C Similarly, A156769 resembles A036279 (from the expansion of tan(x)).
%p a := n -> (-1)^iquo(n,2)*euler(n)*(n+1)/(4^(n+1)-2^(n+1));
%p seq(numer(a(2*n)),n=0..13);
%Y Cf. A009843, A122045, A160144, A160145, A036279, A156769.
%K frac,nonn
%O 0,2
%A _Peter Luschny_, May 03 2009
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