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A264635
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Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.
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7
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1, 1, 1, 1, 2, 4, 8, 16, 48, 144, 432, 1296, 5184, 20736, 82944, 331776, 1658880, 8294400, 41472000, 207360000, 1244160000, 7464960000, 44789760000, 268738560000, 1881169920000, 13168189440000, 92177326080000, 645241282560000, 5161930260480000
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = Product_{i=0..3} floor((n+i)/4)!. - Alois P. Heinz, Jul 12 2016
Sum_{n>0} floor((n-1)/4)/a(n) = 1. - Peter McNair, May 29 2022
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EXAMPLE
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All solutions for n=6:
0 4 4 0
4 0 0 4
1 1 5 5
5 5 1 1
2 2 2 2
3 3 3 3
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MATHEMATICA
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Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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