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

0,5

Comments

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

Links

Table of n, a(n) for n=0..27.

Formula

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

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

Example

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.

Sequence in context: A243793 A001551 A363509 * A145453 A346754 A333916

Adjacent sequences: A067139 A067140 A067141 * A067143 A067144 A067145

Keyword

nonn

Author

Naohiro Nomoto, Feb 19 2002

Extensions

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

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

Status

approved