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A325472 Numbers having at least two representations as multinomial coefficients M(n;lambda), where lambda is a partition of n.

%I A325472 #27 Sep 07 2019 23:50:27
%S A325472 1,6,10,12,15,20,21,24,28,30,35,36,42,45,55,56,60,66,70,72,78,84,90,
%T A325472 91,105,110,120,126,132,136,140,153,156,165,168,171,180,182,190,210,
%U A325472 220,231,240,252,253,272,276,280,286,300,306,325,330,336,342,351,360
%N A325472 Numbers having at least two representations as multinomial coefficients M(n;lambda), where lambda is a partition of n.
%C A325472 Numbers that are repeated in the triangle A036038 (all positive integers occur at least once).
%C A325472 All triangular numbers (A000217) except 0 and 3 are in this sequence.
%H A325472 Alois P. Heinz, <a href="/A325472/b325472.txt">Table of n, a(n) for n = 1..20000</a>
%H A325472 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</a>
%H A325472 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%F A325472 a(n) = A305188(n-1) for n > 1.
%e A325472 1 is in the sequence because M(0;0) = M(1;1) = M(2;2) = M(3;3) = ... = 1.
%e A325472 6 is in the sequence because M(6;5,1) = M(4;2,2) = M(3;1,1,1) = 6.
%e A325472 42 is in the sequence because M(42;41,1) = M(7;5,1,1) = 42.
%Y A325472 Cf. A000041, A000217, A036038, A305188, A325306, A325593, A325901.
%K A325472 nonn
%O A325472 1,2
%A A325472 _Alois P. Heinz_, Sep 06 2019