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%I #6 Jan 27 2020 02:46:34
%S 1,1,3,15,97,777,7379,80983,1007137,13986289,214383171,3593224767,
%T 65347120705,1281151315641,26928292883795,603928982033863,
%U 14392387319349697,363135896514611041,9669298448057196291,270932711729869233903,7967970654277850949025
%N E.g.f.: exp(1 / (1 - tan(x)) - 1).
%F E.g.f.: exp(sin(x) / (cos(x) - sin(x))).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * 2^(k-1) * A000111(k) * a(n-k).
%F a(n) ~ 2^(2*n - 1/4) * exp(1/Pi - 1/2 + 2^(3/2)*sqrt(n/Pi) - n) * n^(n - 1/4) / Pi^(n + 1/4). - _Vaclav Kotesovec_, Jan 27 2020
%t nmax = 20; CoefficientList[Series[Exp[1/(1 - Tan[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A000111[n_] := If[EvenQ[n], Abs[EulerE[n]], Abs[(2^(n + 1) (2^(n + 1) - 1) BernoulliB[n + 1])/(n + 1)]]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] 2^(k - 1) A000111[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%Y Cf. A000111, A000828, A003707, A004211, A006229, A331607.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 22 2020
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