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A193472 Numerator 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 A193472 #14 Jun 24 2019 04:26:34
%S A193472 1,1,1,3,1,25,1,427,1,12465,5,555731,691,35135945,7,2990414715,3617,
%T A193472 329655706465,43867,45692713833379,174611,1111113564712575,854513,
%U A193472 1595024111042171723,236364091,387863354088927172625,8553103,110350957750914345093747,23749461029
%N A193472 Numerator 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 A193472 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/TheLostBernoulliNumbers">The lost Bernoulli numbers.</a>
%p A193472 gf := (f,n) -> coeff(series(f(x),x,n+1),x,n):
%p A193472 BG := n ->`if`(n=0,1,gf(sec+tan,n-1)*n!/(4^n-2^n)):
%p A193472 A193472 := n -> numer(BG(n)): seq(A193472(n),n=0..28);
%t A193472 ez[n_] := SeriesCoefficient[Sec[t] + Tan[t], {t, 0, n}];
%t A193472 a[0] = 1; a[n_] := Numerator[ez[n-1] n!/(4^n - 2^n)];
%t A193472 Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Jun 24 2019 *)
%Y A193472 Cf. A000367, A002445, A009843, A193475, A193473.
%K A193472 nonn,frac
%O A193472 0,4
%A A193472 _Peter Luschny_, Aug 07 2011