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A338438 a(n) = n! * [x^n] Product_{k=1..n, gcd(n,k) = 1} (1 + x^k/k!). 1

%I

%S 1,1,0,3,4,15,6,168,64,171,130,44418,804,802750,2380,683595,5782144,

%T 840363295,40410,24358246734,221953840,3114081516,5372831860,

%U 62269802986834,25703183400,548547778815000,3028000483716,9604167089258628,30673543523224,13242158988496348746

%N a(n) = n! * [x^n] Product_{k=1..n, gcd(n,k) = 1} (1 + x^k/k!).

%t Table[n! SeriesCoefficient[Product[(1 + Boole[GCD[n, k] == 1] x^k/k!), {k, 1, n}], {x, 0, n}], {n, 0, 29}]

%Y Cf. A007837, A036998, A338436.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Oct 27 2020

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)