login
Smallest nonnegative integer k such that there exist n partitions of k which all yield the same multinomial coefficient and with no part appearing in more than one of the partitions.
1

%I #12 Oct 07 2024 15:27:57

%S 0,7,31,50

%N Smallest nonnegative integer k such that there exist n partitions of k which all yield the same multinomial coefficient and with no part appearing in more than one of the partitions.

%e a(2) = 7 is the smallest k such that A376821(k) > 0.

%e | | n partitions of a(n) with a common multinomial coefficient

%e n | a(n) | but no part appearing in more than one of the partitions

%e --+-------+-----------------------------------------------------------

%e 1 | 0 | ()

%e 2 | 7 | (1,1,1,4), (2,2,3)

%e 3 | 31 | (1,1,4,4,4,7,10), (2,2,2,2,5,9,9), (3,3,3,6,8,8)

%e 4 | 50 | (1,1,1,9,12,26), (2,2,8,11,27), (3,3,3,16,25), (5,6,15,24)

%Y Cf. A376661, A376673, A376821.

%K nonn,hard,more

%O 1,2

%A _Pontus von Brömssen_, Oct 05 2024