login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A092043 Numerator of n!/n^2. 5
1, 1, 2, 3, 24, 20, 720, 630, 4480, 36288, 3628800, 3326400, 479001600, 444787200, 5811886080, 81729648000, 20922789888000, 19760412672000, 6402373705728000, 6082255020441600, 115852476579840000, 2322315553259520000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numerator of expansion of dilog(x) = Li_2(x) = - int(0, x, log(1-t)/t*dt). See the Weisstein link.

E.g.f. of {a(n)/A014973(n)}_{n>=1} is Li_2(x) (with 0 for n=0).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

A. N. Kirillov, Dilogarithm identities, arXiv:hep-th/9408113, 1994.

Eric Weisstein's World of Mathematics, Dilogarithm

FORMULA

From Wolfdieter Lang, Apr 28 2017: (Start)

a(n) = numerator(n!/n^2) = numerator((n-1)!/n), n >= 1. See the name.

E.g.f. {a(n)/A014973(n)}_{n>=1} with 0 for n=0 is  Li_2(x). See the comment.

(-1)^n*a(n+1)/A014973(n+1) = (-1)^n*n!/(n+1) = Sum_{k=0..n} Stirling1(n, k)*Bernoulli(k), with Stirling1 = A048994 and Bernoulli(k) = A027641(k)/A027642(k), n >= 0. From inverting the formula for B(k) in terms of Stirling2 = A048993.(End)

MATHEMATICA

Table[Numerator[n!/n^2], {n, 1, 40}] (* Vincenzo Librandi, Apr 15 2014 *)

Table[(n-1)!/n, {n, 30}]//Numerator (* Harvey P. Dale, Apr 03 2018 *)

PROG

(PARI) a(n)=numerator(n!/n^2)

(PARI) a(n)=numerator(polcoeff(serlaplace(dilog(x)), n))

(MAGMA) [Numerator(Factorial(n)/n^2): n in [1..30]]; // Vincenzo Librandi, Apr 15 2014

CROSSREFS

Denominator is in A014973. Cf. A001819.

Sequence in context: A170909 A160606 A099617 * A343206 A055067 A037319

Adjacent sequences:  A092040 A092041 A092042 * A092044 A092045 A092046

KEYWORD

nonn,easy,frac

AUTHOR

Ralf Stephan, Mar 28 2004

EXTENSIONS

Comment rewritten by Wolfdieter Lang, Apr 28 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 26 10:35 EDT 2021. Contains 346294 sequences. (Running on oeis4.)