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).

1, 0, 0, 0, 2, 16, 104, 688, 5116, 44224, 438560, 4851136, 58603544, 764606016, 10715043104, 160692920256, 2570016145680, 43678554864128, 786135111482112, 14936420654180864, 298733557232591136, 6273502048592506112, 138018105454095739008, 3174423293668325353216

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-François Alcover, Jun 16 2018, after Alois P. Heinz *)

Crossrefs

Cf. A187247.

Sequence in context: A207803 A370823 A059204 * A236958 A009619 A012024

Adjacent sequences: A187245 A187246 A187247 * A187249 A187250 A187251

Keyword

nonn

Author

Emeric Deutsch, Mar 07 2011

Status

approved