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

0,3

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.

Example

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.

Crossrefs

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

Column k=3 of A257463.

Sequence in context: A349880 A260339 A205320 * A026025 A231375 A100622

Adjacent sequences: A254240 A254241 A254242 * A254244 A254245 A254246

Keyword

nonn

Author

Tatsuru Murai, Jan 27 2015

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

Status

approved