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!)
A066991 Square array read by descending antidiagonals of number of ways of dividing n*k labeled items into k unlabeled orders with n items in each order. 1
1, 1, 2, 1, 12, 6, 1, 120, 360, 24, 1, 1680, 60480, 20160, 120, 1, 30240, 19958400, 79833600, 1814400, 720, 1, 665280, 10897286400, 871782912000, 217945728000, 239500800, 5040, 1, 17297280, 8892185702400, 20274183401472000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
T(p,k) = (pk)!/k! is divisible by p^k but not p^(k+1) for p prime; e.g., T(3,4) = 3^4*11*10*8*7*5*4*2*1 = 19958400.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..820 (antidiagonals 1..40 of the array, flattened).
FORMULA
T(n,k) = (n*k)!/k!.
EXAMPLE
The array begins:
n\k| 1 2 3 4 ...
--------------------------------------------------------
1 | 1, 1, 1, 1, ...
2 | 2, 12, 120, 1680, ...
3 | 6, 360, 60480, 19958400, ...
4 | 24, 20160, 79833600, 871782912000, ...
5 | 120, 1814400, 217945728000, 101370917007360000, ...
...
MATHEMATICA
Table[((n-k+1)*k)!/k!, {n, 10}, {k, n, 1, -1}] (* Paolo Xausa, Feb 19 2024 *)
CROSSREFS
Rows include A000012, A001813, A064350.
Columns include A000142, A002674, A065961.
Sequence in context: A342587 A008285 A119274 * A132875 A050139 A010255
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Feb 01 2002
EXTENSIONS
Edited by Paolo Xausa, Feb 19 2024
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 April 18 03:29 EDT 2024. Contains 371767 sequences. (Running on oeis4.)