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A186770
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Number of permutations of {1,2,...,n} having no nonincreasing even cycles. A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be even if it has an even number of entries.
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4
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1, 1, 2, 6, 19, 95, 451, 3157, 21092, 189828, 1660351, 18263861, 197541565, 2568040345, 33029787974, 495446819610, 7377279473779, 125413751054243, 2120559951767503, 40290639083582557, 762353357154540584, 16009420500245352264
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: g(z) = exp(cosh z - 1)*sqrt((1+z)/(1-z)).
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EXAMPLE
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a(4)=19 because among the 24 permutations of {1,2,3,4} only (1243), (1324), (1342), (1423), and (1432) have nonincreasing even cycles.
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MAPLE
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g := exp(cosh(z)-1)*sqrt((1+z)/(1-z)): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 21);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
binomial(n-1, j-1)*`if`(j::odd, (j-1)!, 1), j=1..n))
end:
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MATHEMATICA
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a[n_] := a[n] = If[n==0, 1, Sum[a[n-j]*Binomial[n-1, j-1]*If[OddQ[j], (j-1)!, 1], {j, 1, n}]];
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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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