OFFSET
1,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..30
FORMULA
a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2 - 1/12). - Vaclav Kotesovec, Aug 27 2017
a(n) = (n!)^n * [x^n] PolyLog(n,x)/(1 - x), where PolyLog() is the polylogarithm function. - Ilya Gutkovskiy, Nov 27 2017
EXAMPLE
a(3) = 6^3 *(1 + 1/2^3 + 1/3^3) = 251.
MAPLE
MATHEMATICA
Table[(n!)^n * Sum[1/i^n, {i, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Aug 27 2017 *)
PROG
(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
(Magma) [(Factorial(n))^n*(&+[1/j^n: j in [1..n]]): n in [1..15]]; // G. C. Greubel, Apr 09 2021
(Sage) [(factorial(n))^n*sum(1/j^n for j in (1..n)) for n in (1..15)] # G. C. Greubel, Apr 09 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, May 07 2001
STATUS
approved