cp's OEIS Frontend

A376369 Number of nondecreasing tuples (x_1, ..., x_k) of positive integers (or integer partitions) such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) equals n.

%I A376369 #12 Sep 23 2024 11:32:35
%S A376369 1,1,1,1,3,1,1,1,2,1,2,1,1,2,1,1,1,1,3,2,1,1,2,1,1,1,2,1,3,1,1,1,1,2,
%T A376369 2,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,2,3,1,1,1,3,1,1,1,1,1,2,1,1,1,
%U A376369 2,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,2,1,1,1,1,1,1,1,1,1
%N A376369 Number of nondecreasing tuples (x_1, ..., x_k) of positive integers (or integer partitions) such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) equals n.
%C A376369 a(n) is the number of occurrences of n in each of A036038, A050382, A078760, A318762, and A376367.
%C A376369 The sequence is unbounded. To see this, note that the sets of parts (1,1,1,4) and (2,2,3) of a partition can be exchanged without affecting the value of the multinomial coefficient, because 1+1+1+4 = 2+2+3 and 1!*1!*1!*4! = 2!*2!*3!. In particular, a((7*k)!/24^k) >= k+1 from the partitions 7*k = (3*j)*1 + j*4 + (2*(k-j))*2 + (k-j)*3 for 0 <= j <= k.
%H A376369 Pontus von Brömssen, <a href="/A376369/b376369.txt">Table of n, a(n) for n = 2..10000</a>
%e A376369 a(6) = 3, because 6 can be written as a multinomial coefficient in 3 ways: 6 = 6!/(1!*5!) = 4!/(2!*2!) = 3!/(1!*1!*1!).
%Y A376369 Cf. A036038, A050382, A078760, A318762, A376367, A376368, A376370.
%K A376369 nonn
%O A376369 2,5
%A A376369 _Pontus von Brömssen_, Sep 22 2024