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

%I A254243 #40 Apr 18 2020 22:21:29
%S A254243 1,1,2,10,93,1417,32152,1016489,42737945,2307295021,155607773014,
%T A254243 12823004639504,1267907392540573,148160916629902965,
%U A254243 20199662575448858212,3177820001990224608763,571395567211112572679633,116448309072281063992943561,26700057600529091443246943530
%N A254243 Number of ways to partition the multiset consisting of 3 copies each of 1, 2, ..., n into n sets of size 3.
%H A254243 Andrew Howroyd, <a href="/A254243/b254243.txt">Table of n, a(n) for n = 0..100</a>
%H A254243 P. A. MacMahon, <a href="http://plms.oxfordjournals.org/content/s2-17/1/25.extract">Combinations derived from m identical sets of n different letters and their connexion with general magic squares</a>, Proc. London Math. Soc., 17 (1917), 25-41. See page 40 (but there is a typo).
%H A254243 StackExchange, <a href="http://math.stackexchange.com/questions/1126151/number-of-partitioning-a-deck-with-m-cards-in-n-types-into-n-element-sets/1127188#1127188">Number of Partitioning a deck with m cards in n types into n-element sets</a>, January 2015.
%e A254243 a(1) = 1: 111.
%e A254243 a(2) = 2: 111|222 and 112|122.
%e A254243 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.
%Y A254243 Cf. A002135 (2 instead of 3), A254233 (n copies each of 1, 2, and 3).
%Y A254243 Column k=3 of A257463.
%K A254243 nonn
%O A254243 0,3
%A A254243 _Tatsuru Murai_, Jan 27 2015
%E A254243 Name and example edited by _Danny Rorabaugh_, Apr 22 2015
%E A254243 a(6)-a(10) from _Alois P. Heinz_, Apr 22 2015
%E A254243 Terms a(11) and beyond from _Andrew Howroyd_, Apr 18 2020