login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187248 Number of permutations of [n] having only cycles with at least 3 alternating runs (it is assumed that the smallest element of the cycle is in the first position). 4
1, 0, 0, 0, 2, 16, 104, 688, 5116, 44224, 438560, 4851136, 58603544, 764606016, 10715043104, 160692920256, 2570016145680, 43678554864128, 786135111482112, 14936420654180864, 298733557232591136, 6273502048592506112, 138018105454095739008, 3174423293668325353216 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = A187247(n,0).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

E.g.f.: g(z) = exp[(1-2z-exp(2z))/4]/(1-z).

a(n) ~ exp((-1-exp(2))/4) * n!. - Vaclav Kotesovec, Mar 18 2014

EXAMPLE

a(4)=2 because we have (1423) and (1324).

MAPLE

g := exp((1-2*z-exp(2*z))*1/4)/(1-z): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 23);

# second Maple program:

a:= proc(n) option remember;

      `if`(n=0, 1, add(a(n-j)*binomial(n-1, j-1)*

      `if`(j=1, 0, (j-1)!-2^(j-2)), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Apr 15 2017

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Sum[a[n-j]*Binomial[n-1, j-1]* If[j == 1, 0, (j-1)! - 2^(j-2)], {j, 1, n}]];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 16 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A187247.

Sequence in context: A208022 A207803 A059204 * A236958 A009619 A012024

Adjacent sequences:  A187245 A187246 A187247 * A187249 A187250 A187251

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 07 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 26 06:08 EDT 2021. Contains 348257 sequences. (Running on oeis4.)