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 A224290 #20 Nov 28 2018 08:45:39
%S A224290 0,0,0,0,0,1,6,30,136,566,2176,7808,26440,85332,264632,793792,2315136,
%T A224290 6592640,18390784,50392064,135921664,361536512,949708800,2466807808,
%U A224290 6342115328,16153509888,40790523904,102186352640,254105092096,627533152256,1539764125696
%N A224290 Number of permutations of length n containing exactly 3 occurrences of 123 and 3 occurrences of 132.
%H A224290 Alois P. Heinz, <a href="/A224290/b224290.txt">Table of n, a(n) for n = 0..1000</a>
%H A224290 B. Nakamura, <a href="http://arxiv.org/abs/1301.5080">Approaches for enumerating permutations with a prescribed number of occurrences of patterns</a>, arXiv 1301.5080 [math.CO], 2013.
%H A224290 B. Nakamura, <a href="http://www.math.rutgers.edu/~bnaka/GWILF2/F123n132">A Maple package for enumerating n-permutations with r occurrences of the pattern 123 and s occurrences of the pattern 132</a> [Broken link]
%H A224290 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (14,-84,280,-560,672,-448,128).
%F A224290 G.f.: -(4*x^8-8*x^7+24*x^6-36*x^5+62*x^4-60*x^3+30*x^2-8*x+1)*x^5 / (2*x-1)^7. - _Alois P. Heinz_, Apr 03 2013
%F A224290 From _Colin Barker_, Nov 28 2018: (Start)
%F A224290 a(n) = (1/9)*2^(n-15) * (307008 - 247512*n + 78118*n^2 - 12087*n^3 + 937*n^4 - 33*n^5 + n^6) for n>6.
%F A224290 a(n) = 14*a(n-1) - 84*a(n-2) + 280*a(n-3) - 560*a(n-4) + 672*a(n-5) - 448*a(n-6) + 128*a(n-7) for n>13.
%F A224290 (End)
%e A224290 a(5) = 1: (1,4,3,2,5).
%e A224290 a(6) = 6: (2,5,4,3,1,6), (2,5,4,3,6,1), (3,5,1,4,6,2), (3,6,1,4,2,5), (5,1,4,3,2,6), (6,1,4,3,2,5).
%p A224290 # Programs can be obtained from the Nakamura link
%t A224290 Join[{0, 0, 0, 0, 0, 1, 6}, LinearRecurrence[{14, -84, 280, -560, 672, -448, 128}, {30, 136, 566, 2176, 7808, 26440, 85332}, 33]] (* _Jean-François Alcover_, Nov 28 2018 *)
%o A224290 (PARI) concat([0,0,0,0,0], Vec(x^5*(1 - 8*x + 30*x^2 - 60*x^3 + 62*x^4 - 36*x^5 + 24*x^6 - 8*x^7 + 4*x^8) / (1 - 2*x)^7 + O(x^40))) \\ _Colin Barker_, Nov 28 2018
%Y A224290 Cf. A000079, A001787, A001815, A046718, A001793.
%K A224290 nonn
%O A224290 0,7
%A A224290 _Brian Nakamura_, Apr 03 2013