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%I #28 Aug 21 2022 14:10:20
%S 1,6,222,331824,24883200120,139314069504005400,
%T 82606411253903523840005040,6984964247141514123629140377623274720,
%U 109110688415571316480344899355894085582848000725760,395940866122425193243875570782668457763038822400000006270570482400
%N a(n) = n! * Sum_{d|n} (d!)^(d - n/d).
%F E.g.f.: Sum_{k>=1} (k! * x)^k/(k! - x^k).
%t a[n_] := n! * DivisorSum[n, (#!)^(# - n/#) &]; Array[a, 10] (* _Amiram Eldar_, Aug 21 2022 *)
%o (PARI) a(n) = n!*sumdiv(n, d, d!^(d-n/d));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k!*x)^k/(k!-x^k))))
%Y Cf. A061095, A345465, A351165, A356662.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Aug 21 2022
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