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Numbers that occur exactly 4 times in A036038, i.e., numbers m such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) is equal to m for exactly 4 integer partitions (x_1, ..., x_k).
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%I #6 Sep 23 2024 11:33:32

%S 420,630,840,1980,3003,7140,7560,9240,13860,15120,25200,43680,53130,

%T 55440,72072,90090,116280,120120,142506,277200,278256,332640,371280,

%U 415800,450450,480480,813960,1113840,1261260,1801800,2018940,2441880,2702700,3255840,3326400

%N Numbers that occur exactly 4 times in A036038, i.e., numbers m such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) is equal to m for exactly 4 integer partitions (x_1, ..., x_k).

%C Numbers m such that A376369(m) = 4, i.e., numbers that appear exactly 4 times in A376367.

%H Pontus von Brömssen, <a href="/A376374/b376374.txt">Table of n, a(n) for n = 1..10000</a>

%e 420 is a term, because it can be represented as a multinomial coefficient in exactly 4 ways: 420 = 420!/(1!*419!) = 21!/(1!*1!*19!) = 8!/(2!*2!*4!) = 7!/(1!*1!*2!*3!).

%Y Fourth row of A376370.

%Y Cf. A036038, A376367, A376369.

%K nonn

%O 1,1

%A _Pontus von Brömssen_, Sep 23 2024