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!)
A339031 T(n, k) = k*P(n, k), where P(n, k) is the number of partitions of an n-set with k blocks, the largest of which has the size n - k + 1. Triangle T(n, k) for 0 <= k <= n, read by rows. 2
1, 0, 1, 0, 1, 2, 0, 1, 6, 3, 0, 1, 8, 18, 4, 0, 1, 10, 30, 40, 5, 0, 1, 12, 45, 80, 75, 6, 0, 1, 14, 63, 140, 175, 126, 7, 0, 1, 16, 84, 224, 350, 336, 196, 8, 0, 1, 18, 108, 336, 630, 756, 588, 288, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
T(n, k) = k*binomial(n, k - 1) for n >= 1 and 0 < k < n, and T(n, 0) = 0^n, T(n, n) = n.
EXAMPLE
Triangle starts:
0: [1]
1: [0, 1]
2: [0, 1, 2]
3: [0, 1, 6, 3]
4: [0, 1, 8, 18, 4]
5: [0, 1, 10, 30, 40, 5]
6: [0, 1, 12, 45, 80, 75, 6]
7: [0, 1, 14, 63, 140, 175, 126, 7]
8: [0, 1, 16, 84, 224, 350, 336, 196, 8]
9: [0, 1, 18, 108, 336, 630, 756, 588, 288, 9]
.
T(4, 1) = 1 = 1*card({1234})
T(4, 2) = 8 = 2*card({123|4, 124|3, 134|2, 1|234})
T(4, 3) = 18 = 3*card({12|3|4, 13|2|4, 1|23|4, 14|2|3, 1|24|3, 1|2|34})
T(4, 4) = 4 = 4*card({1|2|3|4})
MAPLE
A339031 := proc(n, k) if k = 0 then 0^n elif k = n then n
else k*binomial(n, k-1) fi end:
seq(seq(A339031(n, k), k=0..n), n=0..9);
PROG
(SageMath) # Shows the combinatorial interpretation.
def A339031Row(n):
if n == 0: return [1]
M = matrix(n + 2)
for k in (1..n):
for p in SetPartitions(n):
if p.max_block_size() == k:
M[len(p), k] += p.cardinality()
return [M[k, n-k+1] for k in (0..n)]
for n in (0..9): print(A339031Row(n))
CROSSREFS
Cf. A339032 (row sums), A339030.
Sequence in context: A175197 A367795 A343825 * A367270 A365770 A059299
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 22 2020
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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)