A358411 a(n) = Sum_{d|n} (d + n/d - 1)!/(d - 1)!.
1, 4, 9, 34, 125, 762, 5047, 40468, 362949, 3629560, 39916811, 479007174, 6227020813, 87178331590, 1307674370745, 20922790251808, 355687428096017, 6402373709377404, 121645100408832019, 2432902008216565330, 51090942171709621965, 1124000727778086681754
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (# + n/# - 1)!/(# - 1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)
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PARI
a(n) = sumdiv(n, d, (d+n/d-1)!/(d-1)!);
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-x^k)^(k+1)))
Formula
G.f.: Sum_{k>0} k! * x^k/(1 - x^k)^(k+1).
If p is prime, a(p) = p + p!.