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A185209 Triangle read by rows: T(n,k) is the number of indecomposable (connected) permutations of {1,2,...,n} having genus k (see first comment for definition of genus). 3
1, 1, 0, 2, 1, 0, 5, 8, 0, 0, 14, 49, 8, 0, 0, 42, 268, 151, 0, 0, 0, 132, 1375, 1760, 180, 0, 0, 0, 429, 6768, 16184, 5712, 0, 0, 0, 0, 1430, 32354, 128578, 102917, 8064, 0, 0, 0, 0, 4862, 151336, 923799, 1379384, 369944, 0, 0, 0, 0, 0, 16796, 696027, 6164460, 15283308, 9233512, 604800, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The genus g(p) of a permutation p of {1,2,...,n} is defined by g(p)=(1/2)[n+1-z(p)-z(cp')], where p' is the inverse permutation of p, c = 234...n1 = (1,2,...,n), and z(q) is the number of cycles of the permutation q.

Row sums are A003319.

First column is A000108.

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

Triangle starts:

[ 1]  1,

[ 2]  1, 0,

[ 3]  2, 1, 0,

[ 4]  5, 8, 0, 0,

[ 5]  14, 49, 8, 0, 0,

[ 6]  42, 268, 151, 0, 0, 0,

[ 7]  132, 1375, 1760, 180, 0, 0, 0,

[ 8]  429, 6768, 16184, 5712, 0, 0, 0, 0,

[ 9]  1430, 32354, 128578, 102917, 8064, 0, 0, 0, 0,

[10]  4862, 151336, 923799, 1379384, 369944, 0, 0, 0, 0, 0,

[11]  16796, 696027, 6164460, 15283308, 9233512, 604800, 0, 0, 0, 0, 0,

[12]  58786, 3158280, 38863188, 147930256, 165848135, 36885312, 0, 0, ...,

[13]  208012, 14173566, 234193764, 1293232525, 2397551416, 1193273372, 68428800, 0, ...,

...

CROSSREFS

Cf. A177267 (genus of all permutations).

Cf. A178514 (genus of derangements), A178515 (genus of involutions), A178516 (genus of up-down permutations), A178517 (genus of non-derangement permutations), A178518 (permutations of [n] having genus 0 and p(1)=k).

Sequence in context: A292323 A059720 A140589 * A316659 A241218 A266904

Adjacent sequences:  A185206 A185207 A185208 * A185210 A185211 A185212

KEYWORD

nonn,hard,tabl

AUTHOR

Joerg Arndt, Nov 01 2012

STATUS

approved

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Last modified October 16 23:12 EDT 2018. Contains 316275 sequences. (Running on oeis4.)