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A011553 Number of standard Young tableaux of type (n,n,n) whose (2,1) entry is odd.

%I A011553 #24 Nov 22 2023 06:04:29
%S A011553 0,2,16,182,2400,35310,562848,9540674,169777504,3142665968,
%T A011553 60099912320,1181283863632,23767586624960,487947659276790,
%U A011553 10195163202404160,216335108170636650,4653803620322450880,101343766487960918460,2231268469684932939360,49614581272087698764820
%N A011553 Number of standard Young tableaux of type (n,n,n) whose (2,1) entry is odd.
%D A011553 For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.
%H A011553 Alois P. Heinz, <a href="/A011553/b011553.txt">Table of n, a(n) for n = 1..200</a>
%H A011553 <a href="/index/Y#Young">Index entries for sequences related to Young tableaux.</a>
%F A011553 a(n) ~ 3^(3*n+7/2) / (64*Pi*n^4). - _Vaclav Kotesovec_, Sep 06 2014
%F A011553 Conjecture D-finite with recurrence 6*(n+2)*(n+1)^2*a(n) -(n+1)*(164*n^2-179*n+51) *a(n-1) +(46*n^3-609*n^2+812*n+12) *a(n-2) +12*(3*n-4) *(2*n-5) *(3*n-5)*a(n-3)=0. - _R. J. Mathar_, Nov 22 2023
%e A011553 a(2) = 2 because the standard Young tableaux of type (2,2,2) whose (2,1) entry is odd are:
%e A011553 +---+   +---+
%e A011553 |1 2|   |1 2|
%e A011553 |3 5|   |3 4|
%e A011553 |4 6|   |5 6|
%e A011553 +---+   +---+  - _Alois P. Heinz_, Feb 28 2012
%Y A011553 Cf. A123555.
%K A011553 nonn
%O A011553 1,2
%A A011553 giambruno(AT)ipamat.math.unipa.it
%E A011553 Definition corrected by Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006
%E A011553 More terms and offset corrected by _Alois P. Heinz_, Feb 28 2012