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A067136
Number of Young tableaux with n cells whose shape is symmetric.
3
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, 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
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Feb 19 2002
EXTENSIONS
Edited by Franklin T. Adams-Watters, Nov 07 2006
STATUS
approved