A376673 -id:A376673 - cp's OEIS frontend

A376667 Square array read by antidiagonals: row n lists numbers whose maximal frequency in a fixed row of A036038 (or A078760) is equal to n, i.e., numbers m such that A376663(m) = n.

1, 2, 56, 3, 210, 166320, 4, 504, 360360, 4084080, 5, 1260, 720720, 17907120, 1396755360, 6, 1365, 2162160, 73513440, 4190266080, 698377680, 7, 1680, 5045040, 75675600, 4655851200, 13967553600, 146659312800, 8, 1716, 5765760, 220540320, 4942365120, 27935107200, 293318625600, 1075501627200

Offset: 1

Pontus von Brömssen, Oct 02 2024

In case there are only finitely many solutions for a certain value of n, the rest of that row is filled with 0's.

Each positive integer appears exactly once in the array, so as a linear sequence it is a permutation of the positive integers (unless there are any 0's).

			Array begins:
  n\k|             1             2              3              4              5              6
  ---+----------------------------------------------------------------------------------------
  1  |             1             2              3              4              5              6
  2  |            56           210            504           1260           1365           1680
  3  |        166320        360360         720720        2162160        5045040        5765760
  4  |       4084080      17907120       73513440       75675600      220540320      411863760
  5  |    1396755360    4190266080     4655851200     4942365120     9884730240    24443218800
  6  |     698377680   13967553600    27935107200   267711444000   537750813600   586637251200
  7  |  146659312800  293318625600  1606268664000  3226504881600  6184134356400  7228208988000
  8  | 1075501627200 6453009763200 12368268712800 24736537425600 29683844910720 74209612276800

Pontus von Brömssen, Table of n, a(n) for n = 1..465 (antidiagonals 1..30)

Cf. A036038, A078760, A325306 (complement of first row), A376370, A376663, A376673 (first column).

First five rows are A376668, A376669, A376670, A376671, A376672.

A376666 Indices of records in A376663.

Original entry on oeis.org

1, 56, 166320, 4084080, 698377680, 146659312800, 1075501627200, 37104806138400, 296838449107200, 86825246363856000, 96472495959840000, 35251050023725536000, 272194921062320256000, 408292381593480384000, 4082923815934803840000, 15106818118958774208000

Offset: 1

Pontus von Brömssen, Oct 02 2024

nonn

Pontus von Brömssen, Table of n, a(n) for n = 1..25

Cf. A376378, A376663, A376665, A376673.

a(n) = A376673(A376665(n)).

A376665 Records in A376663.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 20, 21, 23, 25, 28, 30, 31, 33, 38, 41

Offset: 1

Pontus von Brömssen, Oct 02 2024

Cf. A376377, A376663, A376666, A376673.

a(n) = A376663(A376666(n)).

A376828 a(n) = smallest integer k >= 0 such that there exist n disjoint partitions of k that yield the same multinomial coefficient.

Original entry on oeis.org

0, 7, 31, 50

Offset: 1

Pontus von Brömssen, Oct 05 2024

a(5) > 153 if it exists. - Max Alekseyev, May 18 2025

			a(2) = 7 is the smallest k such that A376821(k) > 0.
    |       | n partitions of a(n) with a common multinomial coefficient
  n |  a(n) |  but no part appearing in more than one of the partitions
  --+-------+-----------------------------------------------------------
  1 |    0  | ()
  2 |    7  | (1,1,1,4), (2,2,3)
  3 |   31  | (1,1,4,4,4,7,10), (2,2,2,2,5,9,9), (3,3,3,6,8,8)
  4 |   50  | (1,1,1,9,12,26), (2,2,8,11,27), (3,3,3,16,25), (5,6,15,24)

Cf. A376661, A376673, A376821, A376866.

Name edited by Max Alekseyev, May 18 2025

cp's OEIS Frontend

A376667 Square array read by antidiagonals: row n lists numbers whose maximal frequency in a fixed row of A036038 (or A078760) is equal to n, i.e., numbers m such that A376663(m) = n.

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A376666 Indices of records in A376663.

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A376665 Records in A376663.

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A376828 a(n) = smallest integer k >= 0 such that there exist n disjoint partitions of k that yield the same multinomial coefficient.

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