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.

A067142 One half of the number of Young tableaux with n cells whose shape is asymmetric.

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%I A067142 #14 Jan 13 2020 00:01:39
%S A067142 0,0,1,1,4,10,30,106,316,1254,4140,17128,63856,271492,1126216,4936608,
%T A067142 22278712,101330506,487735440,2313734596,11706759352,58073844300,
%U A067142 305941244576,1587272257096,8656011151184,46886237603400,263791190603200,1487539434072976
%N A067142 One half of the number of Young tableaux with n cells whose shape is asymmetric.
%C A067142 Equivalently, the row lengths are a non-self-conjugate partition of n.
%F A067142 a(n) = (A000085(n) - A067136(n))/2.
%F A067142 a(n) = A330645(n)/2. - _Omar E. Pol_, Jan 11 2020
%e A067142 a(4) = 4 = 8/2; the 8 tableaux are:
%e A067142 1..1234..123..124..134..14..12..13
%e A067142 2........4....3....2....2...3...2.
%e A067142 3.......................3...4...4.
%e A067142 4.................................
%e A067142 The two tableaux of size 4 with symmetric shape are excluded:
%e A067142 12..13
%e A067142 34..24
%Y A067142 Cf. A000085, A000700, A000701, A067136, A330645.
%K A067142 nonn
%O A067142 0,5
%A A067142 _Naohiro Nomoto_, Feb 19 2002
%E A067142 Edited by _Franklin T. Adams-Watters_, Nov 07 2006
%E A067142 a(26)-a(27) from _Omar E. Pol_, Jan 11 2020