The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #11 May 08 2022 08:45:24
%S 1,0,2,-8,56,-336,3184,-27264,309760,-3297280,48104704,-624745472,
%T 10591523840,-159594803200,3133776259072,-56224864108544,
%U 1249919350046720,-24600643845095424,624022403933077504,-14094091678163140608,381632216575339397120,-9516741266133420605440
%N Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + tan(x).
%t nn = 22; f[x_] := Product[(1 + a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Tan[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A000182, A006973, A009006, A137852, A353583, A353584, A353607, A353608, A353609, A353610.
%K sign
%O 1,3
%A _Ilya Gutkovskiy_, May 07 2022