A376673 Least number whose maximum frequency in a fixed row of A036038 (or A078760) is equal to n, i.e., least number m such that A376663(m) = n, or 0 if no such number exists.

1, 56, 166320, 4084080, 1396755360, 698377680, 146659312800, 1075501627200, 37104806138400, 3710480613840000, 296838449107200, 86825246363856000, 96472495959840000, 36466603472819520000, 35251050023725536000, 272194921062320256000, 408292381593480384000

Offset: 1

Author

Pontus von Brömssen, Oct 02 2024

Keywords

• nonn

Comments

After a(36), the sequence continues (where "?" represents terms that are either 0 or greater than 10^29): ?, 3059734941813910128088320000, ?, ?, 64254433778092112689854720000. After a(41), all terms are either 0 or greater than 10^29.

The terms a(1), a(3), ..., a(15), a(24), a(26), ..., a(36), a(38), a(41) are all in A025487, but a(16), ..., a(23), a(25) are all divisible by 17^2 but not by 13^2.

Examples

			First few terms and their representations as multinomial coefficients (corresponding to partitions with sum A376664(n)):
  a(1) =          1 = 0!;
  a(2) =         56 = 8!/(1!*1!*6!) = 8!/(3!*5!);
  a(3) =     166320 = 12!/(1!*1!*1!*4!*5!) = 12!/(1!*1!*2!*2!*6!) = 12!/(2!*2!*3!*5!);
  a(4) =    4084080 = 17!/(1!*1!*1!*4!*10!) = 17!/(1!*2!*5!*9!) = 17!/(2!*2!*3!*10!) = 17!/(4!*6!*7!);
  a(5) = 1396755360 = 19!/(1!*1!*1!*1!*1!*4!*10!) = 19!/(1!*1!*1!*2!*5!*9!) = 19!/(1!*1!*2!*2!*3!*10!) = 19!/(1!*1!*4!*6!*7!) = 19!/(3!*4!*5!*7!).
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..36

Crossrefs

First column of A376667.

Cf. A025487, A036038, A078760, A376376, A376663, A376664.