A374932 Number T(n,k) of partitions of [n] such that the maximal block element sum equals k; triangle T(n,k), n>=0, n <= k <= A000217(n), read by rows.

1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 6, 6, 8, 9, 9, 5, 3, 3, 1, 1, 1, 12, 14, 20, 31, 26, 32, 19, 14, 11, 10, 5, 3, 3, 1, 1, 1, 26, 31, 59, 78, 111, 108, 113, 76, 67, 57, 39, 39, 21, 16, 12, 10, 5, 3, 3, 1, 1, 1, 57, 84, 140, 260, 321, 458, 427, 500, 326, 300, 284, 229, 182, 159, 107, 79, 64, 46, 41, 23, 17, 12, 10, 5, 3, 3, 1, 1, 1

Offset

0,5

Links

Table of n, a(n) for n=0..92.

Wikipedia, Partition of a set

Example

T(5,7) = 8: 124|3|5, 12|34|5, 13|25|4, 14|25|3, 15|2|34, 1|25|34, 1|2|34|5, 1|25|3|4.
T(6,6) = 12: 123|4|5|6, 12|3|4|5|6, 13|24|5|6, 13|2|4|5|6, 14|23|5|6, 15|23|4|6, 1|23|4|5|6, 14|2|3|5|6, 15|24|3|6, 1|24|3|5|6, 15|2|3|4|6, 1|2|3|4|5|6.
T(6,7) = 14: 124|3|5|6, 12|34|5|6, 13|25|4|6, 16|23|4|5, 14|25|3|6, 16|24|3|5, 15|2|34|6, 16|25|34, 1|25|34|6, 16|2|34|5, 1|2|34|5|6, 16|25|3|4, 1|25|3|4|6, 16|2|3|4|5.
Triangle T(n,k) begins:
  1;
     1;
        1, 1;
           2, 1, 1,  1;
              3, 3,  3,  3,  1,  1,  1;
                 6,  6,  8,  9,  9,  5,  3,  3,  1,  1,  1;
                    12, 14, 20, 31, 26, 32, 19, 14, 11, 10, 5, 3, 3, 1, 1, 1;
                    ...

Crossrefs

Row sums give A000110.

Main diagonal gives A375099.

Number of terms in row n is A000124(n-1) for n>=1.

Reversed rows converge to A294617.

Cf. A000217.

Sequence in context: A124772 A227543 A366920 * A344678 A079415 A126347

Adjacent sequences: A374929 A374930 A374931 * A374933 A374934 A374935

Keyword

nonn,tabf

Author

Alois P. Heinz, Aug 01 2024

Status

approved