A376866 - OEIS

A376866

Smallest integer k >= 2 such that there exist n partitions whose corresponding multinomial coefficients are all equal to k, with no part appearing in more than one of the partitions.

2, 6, 120, 3003, 433866230594439538896000

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

| | n partitions with multinomial coefficient a(n)

n | a(n) | and disjoint sets of parts

--+--------------------------+---------------------------------------------

1 | 2 | (1,1)

2 | 6 | (2,2), (1,5)

3 | 120 | (3,7), (2,14), (1,119)

4 | 3003 | (6,8), (5,10), (2,76), (1,3002)

5 | 433866230594439538896000 | (4,9,13,23), (2,2,8,11,27), (3,3,3,16,25), (5,6,15,24),

| | (1,433866230594439538895999)

CROSSREFS

Cf. A180058, A376369, A376376, A376828.

Sequence in context: A212158 A058251 A180058 * A264470 A039716 A164955

Adjacent sequences: A376863 A376864 A376865 * A376867 A376868 A376869

KEYWORD

nonn,hard,more

AUTHOR

Pontus von Brömssen, Oct 07 2024

STATUS

approved