

A287328


Number of permutations of [n] with exactly n (possibly overlapping) occurrences of the generalized pattern 132 (alternatively: 213, 231, or 312).


2



1, 0, 0, 0, 0, 0, 2, 42, 716, 11115, 166144, 2440438, 35573362, 517145226, 7517489564, 109427233994, 1596263948916, 23344423478564, 342325226476816, 5033781463313268, 74223067319020872, 1097343555359525542, 16265399526715750734, 241690082996256941332
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OFFSET

0,7


COMMENTS

Also number of permutations of [n] with n nestings; also number of permutations of [n] with n crossings.


LINKS



FORMULA



MAPLE

b:= proc(u, o) option remember;
`if`(u+o=0, 1, add(b(uj, o+j1), j=1..u)+
add(expand(b(u+j1, oj)*x^(j1)), j=1..o))
end:
a:= n> coeff(b(n, 0), x, n):
seq(a(n), n=0..30);


MATHEMATICA

b[u_, o_] := b[u, o] = If[u + o == 0, 1, Sum[b[u  j, o + j  1], {j, 1, u}] + Sum[Expand[b[u + j  1, o  j]*x^(j  1)], {j, 1, o}]];
a[n_] := Coefficient[b[n, 0], x, n];


CROSSREFS



KEYWORD

nonn,changed


AUTHOR



STATUS

approved



