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

1, 10, 15, 21, 28, 35, 36, 45, 55, 56, 60, 66, 78, 84, 91, 105, 120, 126, 136, 153, 165, 168, 171, 190, 210, 220, 231, 252, 253, 276, 280, 286, 300, 325, 330, 351, 360, 364, 378, 406, 435, 455, 462, 465, 495, 496, 504, 528, 560, 561, 595, 630, 660, 666, 680

Offset: 1

Author

Alois P. Heinz, Sep 07 2019

Keywords

• nonn

Comments

Numbers that are repeated in the triangle A309992 (all positive integers except 2 occur at least once).

All triangular numbers (A000217) except 0, 3 and 6 are in this sequence.

All terms are also contained in A325472.

Examples

			1 is in the sequence because M(0;0) = M(1;1) = M(2;2) = M(3;3) = ... = 1.
10 is in the sequence because M(10;9,1) = M(5;3,2) = 10.
55 is in the sequence because M(55;54,1) = M(11;9,2) = 55.
105 is in the sequence because M(7;4,2,1) = M(15;13,2) = M(105;104,1) = 105.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Wikipedia, Multinomial coefficients
• Wikipedia, Partition (number theory)

Crossrefs

Cf. A000009, A000217, A309992, A325472, A325903.