This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177483 #26 Feb 21 2025 16:46:46
%S A177483 1,1,2,6,20,85,420,2443,16136,120222,993770,9042451,89725944,
%T A177483 964693717,11168801294,138549935190,1833264311504,25773751694161,
%U A177483 383664263687964,6028473673565695,99710105438401940,1731651866118338766,31505416776034601510,599259743707431667279
%N A177483 Number of permutations of n avoiding the pattern 1231'.
%H A177483 Vaclav Kotesovec, <a href="/A177483/b177483.txt">Table of n, a(n) for n = 0..460</a>
%H A177483 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 A177483 E.g.f.: x*exp(x/2) / (cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2) / sqrt(3)) + 1.
%F A177483 a(n) ~ n! * exp(Pi/(3*sqrt(3))) * (3*sqrt(3)/(2*Pi))^n. - _Vaclav Kotesovec_, Aug 24 2014
%e A177483 For n = 4, we have a(4) = 20 because the only bad permutations are 1234, 1342, 1243 and 2341.
%t A177483 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 A177483 nonn
%O A177483 0,3
%A A177483 Signy Olafsdottir (signy06(AT)ru.is), May 09 2010, May 14 2010
%E A177483 Offset corrected by _Vaclav Kotesovec_, Aug 24 2014
%E A177483 More terms from _Vaclav Kotesovec_, Aug 24 2014