A324209 T(n, k) is the largest number of permutations of a partition of n in k parts. T(n, k) read by antidiagonals, for n >= 1 and 1 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 4, 1, 1, 2, 6, 6, 5, 1, 1, 2, 6, 12, 10, 6, 1, 1, 2, 6, 12, 20, 15, 7, 1, 1, 2, 6, 12, 30, 30, 21, 8, 1, 1, 2, 6, 24, 30, 60, 42, 28, 9, 1, 1, 2, 6, 24, 60, 60, 105, 56, 36, 10, 1, 1, 2, 6, 24, 60, 120, 140, 168, 84, 45, 11

Offset

1,5

Links

Table of n, a(n) for n=1..77.

Example

T(7, 3) = 6 because from the partitions of 7 into 3 parts (1, 1, 5), (1, 2, 4), (1, 3, 3), (2, 2, 3), the largest number of distinct permutations such a partition has is 6 (that's the partition (1, 2, 4)).
Table begins:
  1;
  1,  1;
  1,  2,  1;
  1,  2,  3,  1;
  1,  2,  3,  4,  1;
  1,  2,  6,  6,  5,  1;
  1,  2,  6, 12, 10,  6,  1;
  1,  2,  6, 12, 20, 15,  7,  1;
  ...

Mathematica

f[v_] := Multinomial @@ (Tally@v)[[;; , 2]]; T[n_, k_] := Max @@ f /@ IntegerPartitions[n, {k}]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 06 2019 *)

Crossrefs

Sequence in context: A144328 A128227 A306727 * A228107 A140207 A104763

Adjacent sequences: A324206 A324207 A324208 * A324210 A324211 A324212

Keyword

nonn,tabl

Author

David A. Corneth, Apr 07 2019

Status

approved