cp's OEIS Frontend

A325901 Numbers having at least two representations as multinomial coefficients M(n;lambda), where lambda is a partition of n into distinct parts.

%I A325901 #26 Sep 07 2019 23:48:40
%S A325901 1,10,15,21,28,35,36,45,55,56,60,66,78,84,91,105,120,126,136,153,165,
%T A325901 168,171,190,210,220,231,252,253,276,280,286,300,325,330,351,360,364,
%U A325901 378,406,435,455,462,465,495,496,504,528,560,561,595,630,660,666,680
%N A325901 Numbers having at least two representations as multinomial coefficients M(n;lambda), where lambda is a partition of n into distinct parts.
%C A325901 Numbers that are repeated in the triangle A309992 (all positive integers except 2 occur at least once).
%C A325901 All triangular numbers (A000217) except 0, 3 and 6 are in this sequence.
%C A325901 All terms are also contained in A325472.
%H A325901 Alois P. Heinz, <a href="/A325901/b325901.txt">Table of n, a(n) for n = 1..10000</a>
%H A325901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</a>
%H A325901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e A325901 1 is in the sequence because M(0;0) = M(1;1) = M(2;2) = M(3;3) = ... = 1.
%e A325901 10 is in the sequence because M(10;9,1) = M(5;3,2) = 10.
%e A325901 55 is in the sequence because M(55;54,1) = M(11;9,2) = 55.
%e A325901 105 is in the sequence because M(7;4,2,1) = M(15;13,2) = M(105;104,1) = 105.
%Y A325901 Cf. A000009, A000217, A309992, A325472, A325903.
%K A325901 nonn
%O A325901 1,2
%A A325901 _Alois P. Heinz_, Sep 07 2019