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 A000363 M4018 N1666 #33 Nov 09 2024 17:01:01
%S A000363 5,61,479,3111,18270,101166,540242,2819266,14494859,73802835,
%T A000363 373398489,1881341265,9453340172,47417364268,237571096820,
%U A000363 1189405165908,5951965440609,29775517732665,148927275340835,744793282001995
%N A000363 Number of permutations of [n] with exactly 2 increasing runs of length at least 2.
%D A000363 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
%D A000363 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000363 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000363 Vincenzo Librandi, <a href="/A000363/b000363.txt">Table of n, a(n) for n = 4..1000</a>
%H A000363 Shaoshi Chen, Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang, <a href="https://arxiv.org/abs/2411.02897">Patterns in Multi-dimensional Permutations</a>, arXiv:2411.02897 [math.CO], 2024. See p. 7.
%H A000363 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (14,-75,196,-263,174,-45).
%F A000363 From _Vaclav Kotesovec_, Nov 19 2012: (Start)
%F A000363 a(n) = (5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16.
%F A000363 G.f.: -x^4*(9*x-5)/((x-1)^3*(3*x-1)^2*(5*x-1)). (End)
%F A000363 E.g.f.: exp(x)*(exp(4*x) + exp(2*x)*(1 - 6*x) - 2*(1 - x^2))/16. - _Stefano Spezia_, Nov 09 2024
%t A000363 Table[(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16,{n,4,20}] (* _Vaclav Kotesovec_, Nov 19 2012 *)
%o A000363 (Magma) [(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16: n in [4..30]]; // _Vincenzo Librandi_, May 03 2013
%Y A000363 Contribution from _Johannes W. Meijer_, May 24 2009: (Start)
%Y A000363 The a(n) sequence equals the third left hand column of A008971.
%Y A000363 The a(2*n) sequence equals the third left hand column of A160486.
%Y A000363 (End)
%K A000363 nonn,easy
%O A000363 4,1
%A A000363 _N. J. A. Sloane_
%E A000363 More terms and better definition from _Jon E. Schoenfield_, Mar 25 2010