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A059204
Number of non-unimodal permutations of n items (i.e., those which do not simply go up for the first part and then down for the rest, but at some point go down then up).
41
0, 0, 0, 2, 16, 104, 688, 4976, 40192, 362624, 3628288, 39915776, 478999552, 6227016704, 87178283008, 1307674351616, 20922789855232, 355687428030464, 6402373705596928, 121645100408569856, 2432902008176115712, 51090942171708391424, 1124000727777605582848
OFFSET
0,4
COMMENTS
Number of permutations of [n] minus the number of compositions of n. - Zerinvary Lajos, Oct 16 2006
LINKS
FORMULA
a(n) = n! - ceiling(2^(n-1)) = A000142(n) - A011782(n).
E.g.f.: (1+x)/(2*(1-x))-exp(2*x)/2.
EXAMPLE
a(3) = 2 since the possibilities are {BAC, CAB}. a(4) = 16 since the possibilites are {ACBD, ADBC, BACD, BADC, BCAD, BDAC, CABD, CADB, CBAD, CBDA, CDAB, DABC, DACB, DBAC, DBCA, DCAB}.
MAPLE
a:= n-> n!-ceil(2^(n-1)):
seq(a(n), n=0..30);
MATHEMATICA
nn=30; Range[0, nn]!CoefficientList[Series[1/(1-x)-Exp[2x]/2-1/2, {x, 0, nn}], x] (* Geoffrey Critzer, Mar 17 2014 *)
PROG
(PARI) x= 'x + O('x^50); concat([0, 0, 0], Vec(serlaplace((1+x)/(2*(1-x))-exp(2*x)/2))) \\ G. C. Greubel, Dec 28 2016
CROSSREFS
Sequence in context: A208022 A207803 A370823 * A187248 A236958 A009619
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Jan 17 2001
STATUS
approved