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A187245 Number of permutations of [n] having no cycle with 2 alternating runs (it is assumed that the smallest element of the cycle is in the first position). 3
1, 1, 2, 5, 17, 78, 463, 3315, 27164, 247975, 2492539, 27422698, 328607417, 4266367567, 59686293284, 895068242601, 14320843215019, 243467476610732, 4382635181281015, 83272415871044649, 1665465961530365026, 34974843092354081119, 769445564105823722109 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A187244(n,0).

LINKS

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

FORMULA

E.g.f.: g(z)=exp[(4exp(z)-exp(2z)-3-2z)/4]/(1-z).

a(n) ~ exp(exp(1)-exp(2)/4-5/4) * n! = 0.68455780023755436... * n!. - Vaclav Kotesovec, Mar 15 2014

EXAMPLE

a(3)=5 because we have among the 6 permutations of {1,2,3} only 312=(132) has a cycle with 2 alternating runs.

MAPLE

g := exp((4*exp(z)-exp(2*z)-3-2*z)*1/4)/(1-z): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 22);

# second Maple program:

a:= proc(n) option remember;

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

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

    end:

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

MATHEMATICA

CoefficientList[Series[E^((4*E^x-E^(2*x)-3-2*x)/4)/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Mar 15 2014 *)

CROSSREFS

Cf. A187244.

Sequence in context: A199164 A184509 A020096 * A302194 A289739 A243337

Adjacent sequences:  A187242 A187243 A187244 * A187246 A187247 A187248

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 07 2011

STATUS

approved

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Last modified December 1 11:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)