A177483 Number of permutations of n avoiding the pattern 1231'.

1, 1, 2, 6, 20, 85, 420, 2443, 16136, 120222, 993770, 9042451, 89725944, 964693717, 11168801294, 138549935190, 1833264311504, 25773751694161, 383664263687964, 6028473673565695, 99710105438401940, 1731651866118338766, 31505416776034601510, 599259743707431667279

Offset: 0

Author

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

Keywords

• nonn

Examples

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..460
• Sergey Kitaev, Segmented partially ordered generalized patterns, Theoretical Computer Science 349(3) (2005), 420-428; see Proposition 7 (p. 424).

Programs

Mathematica

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 *)

Formula

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

a(n) ~ n! * exp(Pi/(3*sqrt(3))) * (3*sqrt(3)/(2*Pi))^n. - Vaclav Kotesovec, Aug 24 2014

Extensions

Offset corrected by Vaclav Kotesovec, Aug 24 2014

More terms from Vaclav Kotesovec, Aug 24 2014