Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A370366
Number A(n,k) of partitions of [k*n] into n sets of size k having no set of consecutive numbers whose maximum (if k>0) is a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
5
1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 9, 8, 0, 0, 1, 0, 34, 252, 60, 0, 0, 1, 0, 125, 5672, 14337, 544, 0, 0, 1, 0, 461, 125750, 2604732, 1327104, 6040, 0, 0, 1, 0, 1715, 2857472, 488360625, 2533087904, 182407545, 79008, 0, 0
(list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
Alois P. Heinz, Antidiagonals n = 0..54, flattened
Wikipedia, Partition of a set
FORMULA
A(n,k) = A060540(n,k) - A370363(n,k) for n,k >= 1.
EXAMPLE
A(2,3) = 9: 124|356, 125|346, 126|345, 134|256, 135|246, 136|245, 145|236, 146|235, 156|234.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, ...
0, 0, 2, 9, 34, 125, ...
0, 0, 8, 252, 5672, 125750, ...
0, 0, 60, 14337, 2604732, 488360625, ...
0, 0, 544, 1327104, 2533087904, 5192229797500, ...
MAPLE
A:= proc(n, k) `if`(k=0, `if`(n=0, 1, 0), add(
(-1)^(n-j)*binomial(n, j)*(k*j)!/(j!*k!^j), j=0..n))
end:
seq(seq(A(n, d-n), n=0..d), d=0..10);
CROSSREFS
Columns k=0+1,2-3 give: A000007, A053871, A370357.
Rows n=0-2 give: A000012, A000004, A010763(n-1) for k>0.
Main diagonal gives A370367.
Antidiagonal sums give A370368.
Cf. A060540, A370363.
Sequence in context: A365712 A349914 A354105 * A342419 A226350 A373898
Adjacent sequences: A370363 A370364 A370365 * A370367 A370368 A370369
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Feb 16 2024
STATUS
approved

Lookup Welcome Wiki Register Music Plot 2 Demos Index WebCam Contribute Format Style Sheet Transforms Superseeker Recents
The OEIS Community
Maintained by The OEIS Foundation Inc.
Last modified October 21 09:02 EDT 2024. Contains 376980 sequences.
License Agreements, Terms of Use, Privacy Policy