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A060943 a(n) = n!^n * Sum_{k=1..n} 1/k^n. 4
1, 5, 251, 357904, 25795462624, 141727869124448256, 83296040059942781485105152, 7013444132843374500928464765799366656, 109329825340451764123791003609208862665771818418176, 396334659032531033249146049131230887376087800711479296000000000000 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A036740.

Main diagonal of A291556.

Sequence in context: A213446 A276485 A308295 * A336295 A332125 A308652

Adjacent sequences:  A060940 A060941 A060942 * A060944 A060945 A060946

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, May 07 2001

STATUS

approved

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Last modified December 2 17:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)