A349424 Integers that are the product of two factorials A000142.

1, 2, 4, 6, 12, 24, 36, 48, 120, 144, 240, 576, 720, 1440, 2880, 4320, 5040, 10080, 14400, 17280, 30240, 40320, 80640, 86400, 120960, 241920, 362880, 518400, 604800, 725760, 967680, 2177280, 3628800, 4838400, 7257600, 8709120, 21772800, 25401600, 29030400

Offset: 1

Author

Frank M Jackson, Nov 17 2021

Keywords

• nonn

Comments

The first term a(1) = 0!*0! = 1!*0! = 1!*1!.

This is also the number of perfect matchings in a graph connecting C-G and A-U pairs in a RNA string (see Rosalind link). - Lorenzo Pieri, Mar 02 2023

Examples

			720 is a term since 720 = 5!*3! = 6!*0! = 6!*1!.
		

Links

• Rosalind, Perfect Matchings and RNA Secondary Structures.

Crossrefs

Cf. A000142, A098361.

Subsequence of A001013.

Programs

Mathematica

(Union@Flatten@Table[x!*y!, {x, 0, 100}, {y, 0, x}])[[1 ;; 50]]

PARI

lista(nn) = select(x->(x<2*nn!), setbinop((x,y)->x!*y!, [1..nn])); \\ Michel Marcus, Nov 17 2021