

A254243


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


5



1, 1, 2, 10, 93, 1417, 32152, 1016489, 42737945, 2307295021, 155607773014, 12823004639504, 1267907392540573, 148160916629902965, 20199662575448858212, 3177820001990224608763, 571395567211112572679633, 116448309072281063992943561, 26700057600529091443246943530
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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), 2541. See page 40 (but there is a typo).
StackExchange, Number of Partitioning a deck with m cards in n types into nelement sets, January 2015.


EXAMPLE

a(1) = 1: 111.
a(2) = 2: 111222 and 112122.
a(3) = 10: 111222333, 111223233, 112122333, 112123233, 112133223, 113122233, 113123223, 113133222, 122123133, and 123123123.


CROSSREFS

Cf. A002135 (2 instead of 3), A254233 (n copies each of 1, 2, and 3).
Column k=3 of A257463.
Sequence in context: A348837 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



