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A358389 a(n) = n * Sum_{d|n} (d + n/d - 2)!/d!.

%I A358389 #17 Nov 13 2022 10:36:18
%S A358389 1,3,7,29,121,745,5041,40425,362917,3629411,39916801,479006233,
%T A358389 6227020801,87178326495,1307674369891,20922790211057,355687428096001,
%U A358389 6402373709009185,121645100408832001,2432902008212933061,51090942171709581289,1124000727778046764823
%N A358389 a(n) = n * Sum_{d|n} (d + n/d - 2)!/d!.
%H A358389 Michael De Vlieger, <a href="/A358389/b358389.txt">Table of n, a(n) for n = 1..449</a>
%F A358389 G.f.: Sum_{k>0} k! * (x/(1 - x^k))^k.
%F A358389 If p is prime, a(p) = 1 + p!.
%t A358389 Table[n*DivisorSum[n, ((# + n/# - 2)!)/(#!) &], {n, 22}] (* _Michael De Vlieger_, Nov 13 2022 *)
%o A358389 (PARI) a(n) = n*sumdiv(n, d, (d+n/d-2)!/d!);
%o A358389 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*(x/(1-x^k))^k))
%Y A358389 Cf. A038507, A343573.
%K A358389 nonn,easy
%O A358389 1,2
%A A358389 _Seiichi Manyama_, Nov 13 2022