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 A177484 #26 Oct 02 2023 20:20:00
%S A177484 0,0,0,0,6,54,468,3864,32032,269696,2321536,20798448,193509888,
%T A177484 1897735488,19460711424,211113010752,2395487617024,28720852065280,
%U A177484 359273073631232,4735262021189376,64904470318448640,934415802987420672,13945275766952386560,217951935041766097920
%N A177484 The number of permutations having one non-overlapping occurrence of 122'1'.
%C A177484 The variable y is responsible for indicating if we want just one non-overlapping occurrence, and the variable x is responsible for the length of the permutation.
%H A177484 Vaclav Kotesovec, <a href="/A177484/b177484.txt">Table of n, a(n) for n = 0..480</a>
%H A177484 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.
%F A177484 E.g.f.: (1/2 + (1/4)*tan(x)*(1 + e^(2*x) + 2*e^x*sin(x)) + (1/2)*e^x*cos(x))/(1 - y*(1 + (x - 1)*(1/2 + (1/4)*tan(x)*(1 + e^(2*x) + 2*e^x*sin(x)) + (1/2)*e^x*cos(x)))).
%F A177484 E.g.f.: (1/2 + 1/2*exp(x)*cos(x) + 1/4*(1 + exp(2*x) + 2*exp(x)*sin(x)) * tan(x)) * (1 + (-1 + x)*(1/2 + 1/2*exp(x)*cos(x) + 1/4*(1 + exp(2*x) + 2*exp(x)*sin(x))*tan(x))). - _Vaclav Kotesovec_, Aug 25 2014
%F A177484 a(n) ~ n! * (exp(Pi) * (Pi - 2) * cosh(Pi/4)^4 - (-1)^n * exp(-Pi) * (Pi + 2) * sinh(Pi/4)^4) * 2^(n+1) * n / Pi^(n+2). - _Vaclav Kotesovec_, Aug 25 2014
%e A177484 a(4) = 6 because the only bad permutations are 1243, 1342, 1432, 2341, 2431, and 3421.
%t A177484 CoefficientList[Series[(1/2 + 1/2*E^(x)*Cos[x] + 1/4*(1 + E^(2*x) + 2*E^(x)*Sin[x])*Tan[x]) * (1 + (x-1)*(1/2 + 1/2*E^(x)*Cos[x] + 1/4*(1 + E^(2*x) + 2*E^(x)*Sin[x])*Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Aug 25 2014 *)
%K A177484 nonn
%O A177484 0,5
%A A177484 Signy Olafsdottir (signy06(AT)ru.is), May 09 2010, May 14 2010
%E A177484 Offset and example corrected by _Vaclav Kotesovec_, Aug 24 2014
%E A177484 More terms from _Vaclav Kotesovec_, Aug 24 2014