A355669 a(n) = n! * Sum_{d|n} (d!)^(d - n/d).
1, 6, 222, 331824, 24883200120, 139314069504005400, 82606411253903523840005040, 6984964247141514123629140377623274720, 109110688415571316480344899355894085582848000725760, 395940866122425193243875570782668457763038822400000006270570482400
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, (#!)^(# - n/#) &]; Array[a, 10] (* Amiram Eldar, Aug 21 2022 *)
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PARI
a(n) = n!*sumdiv(n, d, d!^(d-n/d));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k!*x)^k/(k!-x^k))))
Formula
E.g.f.: Sum_{k>=1} (k! * x)^k/(k! - x^k).