A067142 - OEIS

%I #14 Jan 13 2020 00:01:39

%S 0,0,1,1,4,10,30,106,316,1254,4140,17128,63856,271492,1126216,4936608,

%T 22278712,101330506,487735440,2313734596,11706759352,58073844300,

%U 305941244576,1587272257096,8656011151184,46886237603400,263791190603200,1487539434072976

%N One half of the number of Young tableaux with n cells whose shape is asymmetric.

%C Equivalently, the row lengths are a non-self-conjugate partition of n.

%F a(n) = (A000085(n) - A067136(n))/2.

%F a(n) = A330645(n)/2. - _Omar E. Pol_, Jan 11 2020

%e a(4) = 4 = 8/2; the 8 tableaux are:

%e 1..1234..123..124..134..14..12..13

%e 2........4....3....2....2...3...2.

%e 3.......................3...4...4.

%e 4.................................

%e The two tableaux of size 4 with symmetric shape are excluded:

%e 12..13

%e 34..24

%Y Cf. A000085, A000700, A000701, A067136, A330645.

%K nonn

%O 0,5

%A _Naohiro Nomoto_, Feb 19 2002

%E Edited by _Franklin T. Adams-Watters_, Nov 07 2006

%E a(26)-a(27) from _Omar E. Pol_, Jan 11 2020