A358410 a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.
1, 2, 3, 9, 25, 130, 721, 5069, 40333, 363006, 3628801, 39917607, 479001601, 6227025848, 87178291591, 1307674408449, 20922789888001, 355687428461452, 6402373705728001, 121645100412461861, 2432902008176660217, 51090942171749356812, 1124000727777607680001
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (# + n/# - 2)!/(# - 1)! &]; Array[a, 23] (* Amiram Eldar, Aug 30 2023 *)
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PARI
a(n) = sumdiv(n, d, (d+n/d-2)!/(d-1)!);
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (k-1)!*(x/(1-x^k))^k))
Formula
G.f.: Sum_{k>0} (k-1)! * (x/(1 - x^k))^k.
If p is prime, a(p) = 1 + (p-1)!.