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A185141 a(n) = (n!)^(2*n). 39
1, 1, 16, 46656, 110075314176, 619173642240000000000, 19408409961765342806016000000000000, 6823819180249038753817675898369448345600000000000000, 48789725533845219197010193096946682961355723304326670581760000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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
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.
MATHEMATICA
Table[(n!)^(2 n), {n, 0, 7}] (* T. D. Noe, Jan 24 2012 *)
PROG
(PARI) for(n=0, 5, print1((n!)^(2*n), ", ")) \\ G. C. Greubel, Jun 23 2017
CROSSREFS
Cf. A000142.
Sequence in context: A253912 A017548 A265588 * A087586 A105312 A013758
KEYWORD
nonn,easy
AUTHOR
David Eppstein, Jan 23 2012
STATUS
approved

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Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)