A254243 Number of ways to partition the multiset consisting of 3 copies each of 1, 2, ..., n into n sets of size 3.

1, 1, 2, 10, 93, 1417, 32152, 1016489, 42737945, 2307295021, 155607773014, 12823004639504, 1267907392540573, 148160916629902965, 20199662575448858212, 3177820001990224608763, 571395567211112572679633, 116448309072281063992943561, 26700057600529091443246943530

Offset: 0

Author

Tatsuru Murai, Jan 27 2015

Keywords

• nonn

Examples

			a(1) = 1: 111.
a(2) = 2: 111|222 and 112|122.
a(3) = 10: 111|222|333, 111|223|233, 112|122|333, 112|123|233, 112|133|223, 113|122|233, 113|123|223, 113|133|222, 122|123|133, and 123|123|123.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41. See page 40 (but there is a typo).
• StackExchange, Number of Partitioning a deck with m cards in n types into n-element sets, January 2015.

Crossrefs

Cf. A002135 (2 instead of 3), A254233 (n copies each of 1, 2, and 3).

Column k=3 of A257463.

Extensions

Name and example edited by Danny Rorabaugh, Apr 22 2015

a(6)-a(10) from Alois P. Heinz, Apr 22 2015

Terms a(11) and beyond from Andrew Howroyd, Apr 18 2020