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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 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: A059720 A140589 A331955 * 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 June 5 09:13 EDT 2020. Contains 334829 sequences. (Running on oeis4.)