A067136 Number of Young tableaux with n cells whose shape is symmetric.

1, 1, 0, 2, 2, 6, 16, 20, 132, 112, 1216, 1440, 12440, 25520, 138048, 476320, 1649312, 9138300, 21842944, 182232248, 345145392, 3805004296, 7002149760, 83299368432, 180168275232, 1907968553776, 5402826994176, 45597877829600

Offset

0,4

Comments

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

Links

Sean A. Irvine, Table of n, a(n) for n = 0..100

Sean A. Irvine, Java program (github)

Formula

a(n) = A000085(n) - 2*A067142(n).

a(n) = A000085(n) - A330645(n). - Omar E. Pol, Jan 11 2020

Example

For n = 8; 4+2+1+1 produces 90 tableaux and 3+3+2 produces
42 tableaux. so a(8) = 90+42 = 132.
For n = 5 = 3+1+1 the 6 tableaux are:
123..124..125..135..134..145
4....3....3....2....2....2..
5....5....4....4....5....3..

Crossrefs

Cf. A000085, A000700, A000701, A067142, A330645.

Sequence in context: A233147 A336633 A001464 * A180068 A034439 A230825

Adjacent sequences: A067133 A067134 A067135 * A067137 A067138 A067139

Keyword

nonn

Author

Naohiro Nomoto, Feb 19 2002

Extensions

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

Status

approved