login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304655 a(n) = (n!)^3 * Sum_{k=1..n-1} 1/(k^3*(n-k)^2). 2
0, 0, 8, 81, 2480, 175000, 23825904, 5563712448, 2051674085376, 1124193889529856, 873600549068759040, 927968580453961728000, 1307864687259363065856000, 2386263863328126193631232000, 5521179117888960788194394112000, 15917227342113559040727019683840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

Recurrence: n*(12*n^4 - 108*n^3 + 354*n^2 - 501*n + 260)*a(n) = 2*(n-1)*(24*n^7 - 306*n^6 + 1620*n^5 - 4599*n^4 + 7516*n^3 - 7015*n^2 + 3444*n - 696)*a(n-1) - 6*(n-2)^4*(12*n^7 - 162*n^6 + 906*n^5 - 2700*n^4 + 4583*n^3 - 4378*n^2 + 2163*n - 436)*a(n-2) + 2*(n-3)^4*(n-2)^3*(24*n^7 - 342*n^6 + 2004*n^5 - 6201*n^4 + 10816*n^3 - 10497*n^2 + 5208*n - 1048)*a(n-3) - (n-4)^5*(n-3)^5*(n-2)^3*(12*n^4 - 60*n^3 + 102*n^2 - 69*n + 17)*a(n-4).

a(n)/(n!)^3 ~ Zeta(3)/n^2.

MATHEMATICA

Table[(n!)^3 * Sum[1/(k^3*(n-k)^2), {k, 1, n-1}], {n, 0, 20}]

CROSSREFS

Cf. A052517, A302827, A304589, A304654.

Sequence in context: A026845 A305770 A145921 * A100399 A022504 A104126

Adjacent sequences:  A304652 A304653 A304654 * A304656 A304657 A304658

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 16 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 12:40 EDT 2022. Contains 356932 sequences. (Running on oeis4.)