

A056986


Number of permutations on {1,...,n} containing any given pattern alpha in the symmetric group S_3.


202



0, 0, 1, 10, 78, 588, 4611, 38890, 358018, 3612004, 39858014, 478793588, 6226277900, 87175616760, 1307664673155, 20922754530330, 355687298451210, 6402373228089300, 121645098641568810, 2432902001612519580, 51090942147243172980, 1124000727686125116360
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OFFSET

1,4


COMMENTS

This is welldefined because for all patterns alpha in S_3 the number of permutations in S_n avoiding alpha is the same (the Catalan numbers).  Emeric Deutsch, May 05 2008


LINKS

FindStat  Combinatorial Statistic Finder, The number of occurrences of the pattern [1,2,3] inside a permutation of length at least 3, The number of occurrences of the pattern [1,3,2] in a permutation, The number of occurrences of the pattern [2,1,3] in a permutation, The number of occurrences of the pattern [2,3,1] in a permutation, The number of occurrences of the pattern [3,1,2] in a permutation


FORMULA

E.g.f.: 1/(1  x)  exp(2*x)*(BesselI(0,2*x)  BesselI(1,2*x)).  Ilya Gutkovskiy, Jan 21 2017


EXAMPLE

a(4) = 10 because, taking, for example, the pattern alpha=321, we have 3214, 3241, 1432, 2431, 3421, 4213, 4132, 4231, 4312 and 4321.


MAPLE

a:= n> n! binomial(2*n, n)/(n+1):


MATHEMATICA

n!Binomial[2n, n]/(n+1)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



