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%I #6 May 11 2022 10:37:25
%S 1,-2,1,-28,29,-194,1583,-61328,144153,-1697262,20127867,-191762088,
%T 3978820221,-66586416948,1057400360235,-58260102945024,
%U 370244721585681,-7992573879248406,162968423791332339,-3399970067764816824,88052648301403014789,-2360852841450177138924
%N Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arcsin(x).
%t nn = 22; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcSin[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A001818, A353818, A353873, A353914, A353915.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 10 2022