cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A067136 #17 Dec 03 2023 22:00:53
%S A067136 1,1,0,2,2,6,16,20,132,112,1216,1440,12440,25520,138048,476320,
%T A067136 1649312,9138300,21842944,182232248,345145392,3805004296,7002149760,
%U A067136 83299368432,180168275232,1907968553776,5402826994176,45597877829600
%N A067136 Number of Young tableaux with n cells whose shape is symmetric.
%C A067136 Equivalently, the row lengths are a self-conjugate partition of n.
%H A067136 Sean A. Irvine, <a href="/A067136/b067136.txt">Table of n, a(n) for n = 0..100</a>
%H A067136 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a067/A067136.java">Java program</a> (github)
%F A067136 a(n) = A000085(n) - 2*A067142(n).
%F A067136 a(n) = A000085(n) - A330645(n). - _Omar E. Pol_, Jan 11 2020
%e A067136 For n = 8; 4+2+1+1 produces 90 tableaux and 3+3+2 produces
%e A067136 42 tableaux. so a(8) = 90+42 = 132.
%e A067136 For n = 5 = 3+1+1 the 6 tableaux are:
%e A067136 123..124..125..135..134..145
%e A067136 4....3....3....2....2....2..
%e A067136 5....5....4....4....5....3..
%Y A067136 Cf. A000085, A000700, A000701, A067142, A330645.
%K A067136 nonn
%O A067136 0,4
%A A067136 _Naohiro Nomoto_, Feb 19 2002
%E A067136 Edited by _Franklin T. Adams-Watters_, Nov 07 2006