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A262745 Number of permutations of [n] with an odd number of rises. 2
0, 0, 1, 4, 12, 52, 360, 2656, 20160, 177472, 1814400, 20135296, 239500800, 3102326272, 43589145600, 654789062656, 10461394944000, 177738781376512, 3201186852864000, 60837094646972416, 1216451004088320000, 25542995336828157952, 562000363888803840000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f.: (1/(1-x) -1 -tanh(x))/2.
a(n) = A000142(n) - A128103(n).
EXAMPLE
a(2) = 1: 12.
a(3) = 4: 132, 213, 231, 312.
MAPLE
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);
MATHEMATICA
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];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 01 2021, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A065525 A317281 A190342 * A180381 A149413 A149414
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 29 2015
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)