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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Mar 07 2011
STATUS
approved