A067136 - OEIS

%I #17 Dec 03 2023 22:00:53

%S 1,1,0,2,2,6,16,20,132,112,1216,1440,12440,25520,138048,476320,

%T 1649312,9138300,21842944,182232248,345145392,3805004296,7002149760,

%U 83299368432,180168275232,1907968553776,5402826994176,45597877829600

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

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

%H Sean A. Irvine, <a href="/A067136/b067136.txt">Table of n, a(n) for n = 0..100</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a067/A067136.java">Java program</a> (github)

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

%F a(n) = A000085(n) - A330645(n). - _Omar E. Pol_, Jan 11 2020

%e For n = 8; 4+2+1+1 produces 90 tableaux and 3+3+2 produces

%e 42 tableaux. so a(8) = 90+42 = 132.

%e For n = 5 = 3+1+1 the 6 tableaux are:

%e 123..124..125..135..134..145

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

%e 5....5....4....4....5....3..

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

%K nonn

%O 0,4

%A _Naohiro Nomoto_, Feb 19 2002

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