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A187252 Number of cycles with at least 3 alternating runs in all permutations of [n] (it is assumed that the smallest element of a cycle is in the first position). 1
0, 0, 0, 0, 2, 26, 260, 2508, 25040, 265552, 3018144, 36827872, 481850240, 6743052672, 100629754112, 1596624594688, 26853667866624, 477435143587840, 8949520012611584, 176443253945217024, 3650510179312910336, 79093615773747232768, 1791150489194147512320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = Sum_{k>=0} k * A187250(n,k).

LINKS

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

FORMULA

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

EXAMPLE

a(4) = 2 because among the permutations of {1,2,3,4} only 3421=(1324) and 4312=(1423) have cycles with more than 2 alternating runs.

MAPLE

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

PROG

(PARI) { my(z='z+O('z^33)); concat( [0, 0, 0, 0], Vec(serlaplace(-(1/4)*(2*z-1+exp(2*z)+4*log(1-z))/(1-z)))) } \\ Joerg Arndt, Apr 16 2017

CROSSREFS

Cf. A187246, A187249, A187250.

Sequence in context: A198960 A289263 A296600 * A096233 A126673 A057351

Adjacent sequences:  A187249 A187250 A187251 * A187253 A187254 A187255

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 08 2011

STATUS

approved

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Last modified April 11 02:27 EDT 2021. Contains 342886 sequences. (Running on oeis4.)