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%I #5 Nov 27 2019 12:53:07
%S 1,3,7,49,121,2161,5041,127681,725761,12852001,39916801,2917918081,
%T 6227020801,392423391361,4740319584001,122053759027201,
%U 355687428096001,57808258040332801,121645100408832001,18854997267794688001,289799177540640768001,7306005040298918553601
%N Expansion of e.g.f. Sum_{k>=1} x^k / (k! * (1 - x^k)^k).
%F a(n) = n! * Sum_{d|n} (d + n/d - 2)! / (d! * (d - 1)! * (n/d - 1)!).
%t nmax = 22; CoefficientList[Series[Sum[x^k/(k! (1 - x^k)^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%t a[n_] := n! Sum[(d + n/d - 2)!/(d! (d - 1)! (n/d - 1)!), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]
%Y Cf. A057625, A157019, A327578, A327579.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 27 2019