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A193473 Denominator of ez(n-1)*n!/(4^n-2^n) where ez(n) is the n-th coefficient of sec(t)+tan(t) for n>0, a(0) = 1.

%I A193473 #10 Jun 26 2019 03:05:34
%S A193473 1,2,6,56,30,992,42,16256,30,261632,66,4192256,2730,67100672,6,
%T A193473 1073709056,510,17179738112,798,274877382656,330,628292059136,138,
%U A193473 70368735789056,2730,1125899873288192,6,18014398375264256,870
%N A193473 Denominator of ez(n-1)*n!/(4^n-2^n) where ez(n) is the n-th coefficient of sec(t)+tan(t) for n>0, a(0) = 1.
%H A193473 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/TheLostBernoulliNumbers">The lost Bernoulli numbers.</a>
%p A193473 gf := (f,n) -> coeff(series(f(x),x,n+1),x,n):
%p A193473 BG := n ->`if`(n=0,1,gf(sec+tan,n-1)*n!/(4^n-2^n)):
%p A193473 A193473 := n -> denom(BG(n)): seq(A193473(n),n=0..28);
%t A193473 ez[n_] := SeriesCoefficient[Sec[t] + Tan[t], {t, 0, n}];
%t A193473 a[0] = 1; a[n_] := Denominator[ez[n - 1] n!/(4^n - 2^n)];
%t A193473 Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Jun 26 2019 *)
%Y A193473 Cf. A000367, A002445, A009843, A193475, A193472.
%K A193473 nonn,frac
%O A193473 0,2
%A A193473 Peter Luschny, Aug 07 2011