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Cf. A129871 (without the mod operation).
(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = 1 + prod(k=1, n-1, va[k]) % (n-1); ); va; } \\ Michel Marcus, Aug 23 2020
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1, 1, 2, 3, 3, 4, 1, 3, 1, 1, 7, 6, 1, 12, 1, 10, 1, 12, 1, 3, 1, 1, 21, 12, 1, 6, 21, 1, 1, 15, 1, 20, 1, 31, 15, 1, 1, 32, 13, 1, 1, 18, 1, 7, 25, 1, 17, 38, 1, 1, 1, 1, 1, 26, 1, 6, 1, 1, 29, 47, 1, 42, 1, 1, 1, 1, 61, 26, 1, 25, 1, 21, 1, 64, 21, 1, 1, 29, 1, 18, 1, 1, 11, 21, 1, 1, 59, 1, 1, 39, 1, 1, 5, 1, 1, 1, 1, 32, 1, 1, 1, 42, 1, 9, 1, 1, 29, 55, 1, 44, 1
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1, 1, 2, 3, 3, 4, 1, 3, 1, 1, 7, 6, 1, 12, 1, 10, 1, 12, 1, 3, 1, 1, 21, 12, 1, 6, 21, 1, 1, 15, 1, 20, 1, 31, 15, 1, 1, 32, 13, 1, 1, 18, 1, 7, 25, 1, 17, 38, 1, 1, 1, 1, 1, 26, 1, 6, 1, 1, 29, 47, 1, 42, 1, 1, 1, 1, 61, 26, 1, 25, 1, 21, 1, 64, 21, 1, 1, 29, 1, 18, 1, 1, 11, 21, 1, 1, 59, 1, 1, 39, 1, 1, 5, 1, 1, 1, 1, 32, 1, 1, 1, 42, 1, 9, 1, 1, 29, 55, 1, 44, 1
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a[1] = 1; a[n_] := a[n] = 1 + Mod[Product[a[k], {k, 1, n - 1}], n - 1]; Array[a, 100] (* Amiram Eldar, Aug 22 2020 *)
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