A067142 -id:A067142 - cp's OEIS frontend

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

Naohiro Nomoto, Feb 19 2002

nonn

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

			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..

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

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

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

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

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

A330645 Number of Young tableaux with n cells whose shape is asymmetric.

Original entry on oeis.org

0, 0, 2, 2, 8, 20, 60, 212, 632, 2508, 8280, 34256, 127712, 542984, 2252432, 9873216, 44557424, 202661012, 975470880, 4627469192, 23413518704, 116147688600, 611882489152, 3174544514192, 17312022302368, 93772475206800, 527582381206400, 2975078868145952

Offset: 0

Omar E. Pol, Jan 11 2020

nonn

Cf. A000085, A067136, A067142.

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

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

cp's OEIS Frontend

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

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