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A262745
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Number of permutations of [n] with an odd number of rises.
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2
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0, 0, 1, 4, 12, 52, 360, 2656, 20160, 177472, 1814400, 20135296, 239500800, 3102326272, 43589145600, 654789062656, 10461394944000, 177738781376512, 3201186852864000, 60837094646972416, 1216451004088320000, 25542995336828157952, 562000363888803840000
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: (1/(1-x) -1 -tanh(x))/2.
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EXAMPLE
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a(2) = 1: 12.
a(3) = 4: 132, 213, 231, 312.
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MAPLE
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b:= proc(u, o, t) option remember; `if`(u+o=0, t,
add(b(u-j, o+j-1, t), j=1..u)+
add(b(u+j-1, o-j, 1-t), j=1..o))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..25);
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, t,
Sum[b[u - j, o + j - 1, t], {j, 1, u}] +
Sum[b[u + j - 1, o - j, 1 - t], {j, 1, o}]];
a[n_] := b[n, 0, 0];
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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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