A185141 a(n) = (n!)^(2*n).

1, 1, 16, 46656, 110075314176, 619173642240000000000, 19408409961765342806016000000000000, 6823819180249038753817675898369448345600000000000000, 48789725533845219197010193096946682961355723304326670581760000000000000000

Offset: 0

Author

David Eppstein, Jan 23 2012

Keywords

• nonn
• easy

Comments

a(n) is the number of "templates", or ways of placing a single digit within an n^2*n^2 Sudoku puzzle so that all rows, columns, and n*n blocks have exactly one copy of the digit.

a(n) is the number of preference profiles in a stable marriage problem with n men and n women. - Tanya Khovanova and MIT PRIMES STEP Senior group, Mar 31 2021

a(n) is the product of the elements in the multiplication table [1..n] X [1..n]. - Ivan N. Ianakiev, Oct 04 2022

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..22
• Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, The Stable Matching Problem and Sudoku, arXiv:2108.02654 [math.HO], 2021.
• Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021.
• Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, The Stable Marriage Problem and Sudoku, College Math. J. (2023).
• G. Dahl, Permutation matrices related to Sudoku, Linear Algebra and its Applications, 430 (2001), 2457-2463.
• sudopedia.org, Template

Crossrefs

Cf. A000142.

Programs

Mathematica

Table[(n!)^(2 n), {n, 0, 7}] (* T. D. Noe, Jan 24 2012 *)

PARI

for(n=0,5, print1((n!)^(2*n), ", ")) \\ G. C. Greubel, Jun 23 2017

Formula

a(n) ~ n^(n*(2*n+1)) * 2^n * Pi^n / exp(2*n^2 - 1/6). - Vaclav Kotesovec, Feb 19 2015

Equals 2*n-th power of A000142.