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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.
0
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
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
KEYWORD
nonn,tabl
AUTHOR
David A. Corneth, Apr 07 2019
STATUS
approved