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A337303
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Number of X-based filling of diagonals in a diagonal Latin square of order n.
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2
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1, 1, 0, 0, 96, 480, 57600, 403200, 191600640, 1724405760, 1597368729600, 17571056025600, 28378507272192000, 368920594538496000, 952903592436341145600, 14293553886545117184000, 55442575636536644075520000, 942523785821122949283840000, 5231730206388249282710863872000
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OFFSET
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0,5
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COMMENTS
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Used for getting strong canonical forms (SCFs) of the diagonal Latin squares and for fast enumerating of the diagonal Latin squares based on equivalence classes.
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LINKS
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FORMULA
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EXAMPLE
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One of the 96 X-based fillings of diagonals of a diagonal Latin square for order n=4:
1 . . 0
. 0 1 .
. 3 2 .
2 . . 3
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PROG
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b(n) = {sum(m=0, n, sum(k=0, n-m, (-1)^k * binomial(n, k) * binomial(n-k, m) * 2^(2*k+m-n) * (2*n-2*m-k)! )); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, Mar 26 2023
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STATUS
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approved
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