A067142 One half of the number of Young tableaux with n cells whose shape is asymmetric.

0, 0, 1, 1, 4, 10, 30, 106, 316, 1254, 4140, 17128, 63856, 271492, 1126216, 4936608, 22278712, 101330506, 487735440, 2313734596, 11706759352, 58073844300, 305941244576, 1587272257096, 8656011151184, 46886237603400, 263791190603200, 1487539434072976

Offset: 0

Author

Naohiro Nomoto, Feb 19 2002

Keywords

• nonn

Comments

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

Examples

			a(4) = 4 = 8/2; the 8 tableaux are:
1..1234..123..124..134..14..12..13
2........4....3....2....2...3...2.
3.......................3...4...4.
4.................................
The two tableaux of size 4 with symmetric shape are excluded:
12..13
34..24
		

Crossrefs

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

Formula

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

a(n) = A330645(n)/2. - Omar E. Pol, Jan 11 2020

Extensions

Edited by Franklin T. Adams-Watters, Nov 07 2006

a(26)-a(27) from Omar E. Pol, Jan 11 2020