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A258213
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Number of permutations of {1,2,3,...,n} such that no even numbers are adjacent.
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1
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1, 1, 2, 6, 12, 72, 144, 1440, 2880, 43200, 86400, 1814400, 3628800, 101606400, 203212800, 7315660800, 14631321600, 658409472000, 1316818944000, 72425041920000, 144850083840000, 9560105533440000, 19120211066880000, 1491376463216640000, 2982752926433280000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = factorial(ceiling(n/2))*fallfac(ceiling(n/2)+1, floor(n/2)), with fallfac = A008279.
D-finite with recurrence: (4*(n-2)^2 + 24*n - 80)*a(n) + (16*n+24)*a(n-1) - (n+2)*n*((n-2)^2 + 8*n - 17)*a(n-2) = 0. - Georg Fischer, Nov 23 2022
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MAPLE
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a:= n-> (m-> m!^2*(m+1))(iquo(n+1, 2, 'r'))/(2-r):
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PROG
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(PARI) T(n, k) = n!/(n-k)!; \\ A008279
a(n) = ceil(n/2)!*T(ceil(n/2)+1, n\2); \\ Michel Marcus, Nov 24 2022
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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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