A060943 - OEIS

%I #25 Apr 09 2021 09:16:36

%S 1,5,251,357904,25795462624,141727869124448256,

%T 83296040059942781485105152,7013444132843374500928464765799366656,

%U 109329825340451764123791003609208862665771818418176,396334659032531033249146049131230887376087800711479296000000000000

%N a(n) = n!^n * Sum_{k=1..n} 1/k^n.

%H Harry J. Smith, <a href="/A060943/b060943.txt">Table of n, a(n) for n = 1..30</a>

%F a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2 - 1/12). - _Vaclav Kotesovec_, Aug 27 2017

%F a(n) = (n!)^n * [x^n] PolyLog(n,x)/(1 - x), where PolyLog() is the polylogarithm function. - _Ilya Gutkovskiy_, Nov 27 2017

%e a(3) = 6^3 *(1 + 1/2^3 + 1/3^3) = 251.

%p A060943:= n-> (n!)^n*add(1/j^n, j=1..n); seq(A060943(n), n=1..15); # _G. C. Greubel_, Apr 09 2021

%t Table[(n!)^n * Sum[1/i^n, {i, 1, n}], {n, 1, 10}] (* _Vaclav Kotesovec_, Aug 27 2017 *)

%o (PARI) { default(realprecision, 100); for (n=1, 30, write("b060943.txt", n, " ", n!^n * sum(k=1, n, 1/k^n)); ) } \\ _Harry J. Smith_, Jul 14 2009

%o (Magma) [(Factorial(n))^n*(&+[1/j^n: j in [1..n]]): n in [1..15]]; // _G. C. Greubel_, Apr 09 2021

%o (Sage) [(factorial(n))^n*sum(1/j^n for j in (1..n)) for n in (1..15)] # _G. C. Greubel_, Apr 09 2021

%Y Cf. A036740.

%Y Main diagonal of A291556.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, May 07 2001