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%I #17 Aug 21 2022 14:10:15
%S 1,6,60,1584,75120,5601960,592956000,84557864160,15620794842240,
%T 3628800457682400,1035338990353113600,355902198996315787200,
%U 145077660657865961625600,69194697633957032681544000,38174841090323471644830720000,24122334398251368151021076928000
%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, 16] (* _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. A062796, A087905, A355669, A356661.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Aug 21 2022
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