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A376866 a(n) = smallest integer k >= 2 such that there exist n disjoint multisets of positive integers, whose corresponding multinomial coefficients equal k.

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%I A376866 #22 Jun 12 2025 22:35:54
%S A376866 2,6,120,3003,433866230594439538896000
%N A376866 a(n) = smallest integer k >= 2 such that there exist n disjoint multisets of positive integers, whose corresponding multinomial coefficients equal k.
%e A376866   n |                     a(n) | disjoint multisets with multinomial coefficient a(n)
%e A376866   --+--------------------------+---------------------------------------------
%e A376866   1 |                        2 | {1,1}
%e A376866   2 |                        6 | {2,2}, {1,5}
%e A376866   3 |                      120 | {3,7}, {2,14}, {1,119}
%e A376866   4 |                     3003 | {6,8}, {5,10}, {2,76}, {1,3002}
%e A376866   5 | 433866230594439538896000 | {4,9,13,23}, {2,2,8,11,27}, {3,3,3,16,25}, {5,6,15,24},
%e A376866     |                          | {1,433866230594439538895999}
%Y A376866 Cf. A180058, A376369, A376376, A376828.
%K A376866 nonn,hard,more,nice
%O A376866 1,1
%A A376866 _Pontus von Brömssen_, Oct 07 2024
%E A376866 Edited by _Max Alekseyev_, May 18 2025