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%I #10 May 08 2022 08:45:20
%S 1,5,-14,1777,-14744,247994,-74928944,42293543177,-1163849271296,
%T 95795966018440,-44942000161435904,4494117864138588514,
%U -3539995034294896016384,770158600620174924566672,-510461123036204706738612224,1162153458061287151457003978297
%N Product_{n>=1} (1 + a(n)*x^(2*n)/(2*n)!) = sec(x).
%t nn = 16; f[x_] := Product[(1 + a[n] x^(2 n)/(2 n)!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Sec[x], {x, 0, 2 nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A000364, A006973, A137852, A353607, A353608, A353609, A353611.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 07 2022