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a(n) = n! * Sum_{d|n} (d/n)^d.
3

%I #9 May 17 2018 17:33:29

%S 1,3,8,36,144,1010,5760,50400,416640,4250232,43545600,553106400,

%T 6706022400,95865541200,1410695430144,22720842144000,376610217984000,

%U 6888030445296000,128047474114560000,2587520533615041024

%N a(n) = n! * Sum_{d|n} (d/n)^d.

%H G. C. Greubel, <a href="/A087905/b087905.txt">Table of n, a(n) for n = 1..445</a>

%F E.g.f.: Sum_{k>0} x^k/(k-x^k).

%t a[n_]:= n!*DivisorSum[n, (#/n)^# &]; Array[a, 50] (* _G. C. Greubel_, May 16 2018 *)

%o (PARI) {a(n)= n!*sumdiv(n, d, (d/n)^d)};

%o for(n=1, 30, print1(a(n), ", ")) \\ _G. C. Greubel_, May 16 2018

%Y Cf. A061095, A038041, A057625, A038048, A005225.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Oct 14 2003