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A185141 a(n) = (n!)^(2*n). 3
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.

LINKS

Table of n, a(n) for n=0..8.

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

Adjacent sequences:  A185138 A185139 A185140 * A185142 A185143 A185144

KEYWORD

nonn,easy

AUTHOR

David Eppstein, Jan 23 2012

STATUS

approved

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)