%I #5 Oct 28 2020 09:29:13
%S 1,1,2,9,32,300,864,17612,74752,1152792,6470400,220057992,719622144,
%T 40754156352,192835098624,4787867880000,55181218873344,
%U 3071730630989952,11004144881762304,1179255538492239744,5720352215040000000,253837962769406045184,3262870639485701849088
%N a(n) = n! * [x^n] Product_{k=1..n, gcd(n,k) = 1} 1 / (1 - x^k/k).
%t Table[n! SeriesCoefficient[Product[1/(1 - Boole[GCD[n, k] == 1] x^k/k), {k, 1, n}], {x, 0, n}], {n, 0, 22}]
%Y Cf. A007841, A057562, A338439.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 27 2020