%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