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%I #10 Jun 10 2022 11:07:49
%S 1,3,7,49,121,2521,5041,208321,907201,32810401,39916801,10621860481,
%T 6227020801,2877004690561,19233710496001,1415779600435201,
%U 355687428096001,1085522620595212801,121645100408832001,653741050484890368001,6259137133527742464001,576612373659657208473601
%N a(n) = n! * Sum_{d|n} d^(n/d - 1) / d!.
%H Seiichi Manyama, <a href="/A327578/b327578.txt">Table of n, a(n) for n = 1..425</a>
%F E.g.f.: Sum_{k>=1} x^k / (k! * (1 - k * x^k)).
%t a[n_] := n! Sum[d^(n/d - 1)/d!, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]
%t nmax = 22; CoefficientList[Series[Sum[x^k/(k! (1 - k x^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%o (PARI) a(n) = n! * sumdiv(n, d, d^(n/d - 1) / d!); \\ _Michel Marcus_, Sep 17 2019
%Y Cf. A057625, A087909, A327579.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Sep 17 2019
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