A324209 - OEIS

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.

%I #16 Jul 20 2019 11:04:24

%S 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,

%T 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,

%U 60,105,56,36,10,1,1,2,6,24,60,120,140,168,84,45,11

%N 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.

%e 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)).

%e Table begins:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 2, 3, 1;

%e 1, 2, 3, 4, 1;

%e 1, 2, 6, 6, 5, 1;

%e 1, 2, 6, 12, 10, 6, 1;

%e 1, 2, 6, 12, 20, 15, 7, 1;

%e ...

%t 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 *)

%K nonn,tabl

%O 1,5

%A _David A. Corneth_, Apr 07 2019