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a(1) = 1; a(n) = Sum_{d|n, d < n} binomial(n/d,d) * a(d).
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%I #5 Jun 10 2021 22:37:21

%S 1,2,3,6,5,12,7,20,12,30,11,54,13,56,45,78,17,150,19,140,126,132,23,

%T 414,30,182,279,420,29,630,31,692,528,306,140,1770,37,380,897,1960,41,

%U 1638,43,2486,2040,552,47,5586,56,1910,2091,4992,53,4212,2365,6874,2964,870,59,19020

%N a(1) = 1; a(n) = Sum_{d|n, d < n} binomial(n/d,d) * a(d).

%t a[1] = 1; a[n_] := a[n] = Sum[If[d < n, Binomial[n/d, d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 60}]

%Y Cf. A008578 (fixed points), A074206, A318636, A330017, A345136.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jun 10 2021