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A185141
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a(n) = (n!)^(2*n).
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39
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1, 1, 16, 46656, 110075314176, 619173642240000000000, 19408409961765342806016000000000000, 6823819180249038753817675898369448345600000000000000, 48789725533845219197010193096946682961355723304326670581760000000000000000
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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a(n) ~ n^(n*(2*n+1)) * 2^n * Pi^n / exp(2*n^2 - 1/6). - Vaclav Kotesovec, Feb 19 2015
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MATHEMATICA
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Table[(n!)^(2 n), {n, 0, 7}] (* T. D. Noe, Jan 24 2012 *)
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PROG
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(PARI) for(n=0, 5, print1((n!)^(2*n), ", ")) \\ G. C. Greubel, Jun 23 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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