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%I #6 May 11 2022 10:37:29
%S 1,-2,-1,-20,-11,46,-547,-29840,-27351,232818,-3258663,-29911848,
%T -390445563,4450393260,-84140635815,-12153983817984,-18431412645519,
%U 286688710444842,-6436900596281679,-169286474970429624,-2208721087854287811,41892263643715799796,-1149793471388581053219
%N Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arcsinh(x).
%t nn = 23; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcSinh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A001818, A353819, A353910, A353913, A353915.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 10 2022
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