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Number of permutations avoiding the pattern 1231'.
9

%I #21 Nov 01 2019 03:44:44

%S 1,1,2,6,20,85,420,2443,16136,120222,993770,9042451,89725944,

%T 964693717,11168801294,138549935190,1833264311504,25773751694161,

%U 383664263687964,6028473673565695,99710105438401940,1731651866118338766,31505416776034601510,599259743707431667279

%N Number of permutations avoiding the pattern 1231'.

%H Vaclav Kotesovec, <a href="/A177483/b177483.txt">Table of n, a(n) for n = 0..460</a>

%H Sergey Kitaev, <a href="https://doi.org/10.1016/j.tcs.2005.09.036">Segmented partially ordered generalized patterns</a>, Theoretical Computer Science 349(3) (2005), 420-428; see Proposition 7 (p. 424).

%F E.g.f.: x*exp(x/2) / (cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2) / sqrt(3)) + 1.

%F a(n) ~ n! * exp(Pi/(3*sqrt(3))) * (3*sqrt(3)/(2*Pi))^n. - _Vaclav Kotesovec_, Aug 24 2014

%e For n = 4, we have a(4) = 20 because the only bad permutations are 1234, 1342, 1243 and 2341.

%t CoefficientList[Series[x*E^(x/2)/(Cos[Sqrt[3]*x/2] - Sin[Sqrt[3]*x/2] / Sqrt[3]) + 1,{x,0,20}],x] * Range[0,20]! (* _Vaclav Kotesovec_, Aug 24 2014*)

%K nonn

%O 0,3

%A Signy Olafsdottir (signy06(AT)ru.is), May 09 2010, May 14 2010

%E Offset corrected by _Vaclav Kotesovec_, Aug 24 2014

%E More terms from _Vaclav Kotesovec_, Aug 24 2014