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%I #8 Nov 01 2012 11:13:03
%S 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,
%T 0,0,429,6768,16184,5712,0,0,0,0,1430,32354,128578,102917,8064,0,0,0,
%U 0,4862,151336,923799,1379384,369944,0,0,0,0,0,16796,696027,6164460,15283308,9233512,604800,0
%N 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).
%C 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.
%C Row sums are A003319.
%C First column is A000108.
%e Triangle starts:
%e [ 1] 1,
%e [ 2] 1, 0,
%e [ 3] 2, 1, 0,
%e [ 4] 5, 8, 0, 0,
%e [ 5] 14, 49, 8, 0, 0,
%e [ 6] 42, 268, 151, 0, 0, 0,
%e [ 7] 132, 1375, 1760, 180, 0, 0, 0,
%e [ 8] 429, 6768, 16184, 5712, 0, 0, 0, 0,
%e [ 9] 1430, 32354, 128578, 102917, 8064, 0, 0, 0, 0,
%e [10] 4862, 151336, 923799, 1379384, 369944, 0, 0, 0, 0, 0,
%e [11] 16796, 696027, 6164460, 15283308, 9233512, 604800, 0, 0, 0, 0, 0,
%e [12] 58786, 3158280, 38863188, 147930256, 165848135, 36885312, 0, 0, ...,
%e [13] 208012, 14173566, 234193764, 1293232525, 2397551416, 1193273372, 68428800, 0, ...,
%e ...
%Y Cf. A177267 (genus of all permutations).
%Y 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).
%K nonn,hard,tabl
%O 1,4
%A _Joerg Arndt_, Nov 01 2012
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