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A353821
Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + arctanh(x).
6
1, 0, 2, -8, 64, -384, 3968, -34432, 414720, -4454400, 68247552, -912236544, 15949529088, -245572583424, 5012834549760, -92436465352704, 2119956936523776, -42836227522560000, 1123874181449515008, -26161653829651660800, 730049769522063212544, -18719979459270521389056
OFFSET
1,3
MATHEMATICA
nn = 22; f[x_] := Product[(1 + a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcTanh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 08 2022
STATUS
approved