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A184185 Number of permutations of {1,2,...,n} having no cycles of the form (i, i+1, i+2, ..., i+j-1) (j>=1). 1
1, 0, 0, 1, 6, 34, 216, 1566, 12840, 117696, 1193760, 13280520, 160841520, 2107021680, 29689833600, 447821503920, 7199590366080, 122907276334080, 2220524598297600, 42328747652446080, 849064844592518400, 17877531486897734400, 394246607165708774400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = A184184(n,0).

LINKS

Table of n, a(n) for n=0..22.

Patxi Laborde Zubieta, Occupied corners in tree-like tableaux, arXiv preprint arXiv:1505.06098 [math.CO], 2015.

FORMULA

G.f.: (1-z)*F(z-z^2), where F(z)=Sum(j!z^j, j>=0) (private communication from Vladeta Jovovic, May 26 2009).

a(n) = Sum((-1)^{n-i}*i!*binomial(i+1,n-i), i=ceil((n-1)/2) .. n).

G.f.: 1/Q(0), where Q(k)= 1 + x/(1-x) - x*(k+1)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 19 2013

EXAMPLE

a(4)=6 because we have (13)(24), (1432), (1342), (1423), (1243), and (1324).

MAPLE

a := proc (n) options operator, arrow: sum((-1)^(n-i)*factorial(i)*binomial(i+1, n-i), i = ceil((1/2)*n-1/2) .. n) end proc: seq(a(n), n = 0 .. 22);

MATHEMATICA

a[n_] := Sum[(-1)^(n-i)*i!*Binomial[i+1, n-i], {i, Ceiling[(n-1)/2], n}];

Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Nov 29 2017, from Maple *)

CROSSREFS

Cf. A184184.

Sequence in context: A218893 A266431 A063090 * A216317 A230331 A267242

Adjacent sequences:  A184182 A184183 A184184 * A184186 A184187 A184188

KEYWORD

nonn,changed

AUTHOR

Emeric Deutsch, Feb 16 2011 (based on communication from Vladeta Jovovic)

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.