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

0, 2, 16, 182, 2400, 35310, 562848, 9540674, 169777504, 3142665968, 60099912320, 1181283863632, 23767586624960, 487947659276790, 10195163202404160, 216335108170636650, 4653803620322450880, 101343766487960918460, 2231268469684932939360, 49614581272087698764820

Offset: 1

Author

giambruno(AT)ipamat.math.unipa.it

Keywords

• nonn

Examples

			a(2) = 2 because the standard Young tableaux of type (2,2,2) whose (2,1) entry is odd are:
+---+   +---+
|1 2|   |1 2|
|3 5|   |3 4|
|4 6|   |5 6|
+---+   +---+  - _Alois P. Heinz_, Feb 28 2012
		

References

• For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200
• Index entries for sequences related to Young tableaux.

Crossrefs

Cf. A123555.

Formula

a(n) ~ 3^(3*n+7/2) / (64*Pi*n^4). - Vaclav Kotesovec, Sep 06 2014

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

Extensions

Definition corrected by Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006

More terms and offset corrected by Alois P. Heinz, Feb 28 2012