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 A132647 #12 Feb 17 2024 08:40:56
%S A132647 1,1,2,6,23,117,706,4962,39817,359171,3597936,39630372,476066277,
%T A132647 6194080387,86776390796,1302376048620,20847721870931,354549730559949,
%U A132647 6384006047649910,121330369923079290,2427196999663678987,50981866833670160201,1121806937829102793662
%N A132647 Number of permutations of [n] having no substring [k,k+1,k+2,k+3].
%H A132647 Andrew Howroyd, <a href="/A132647/b132647.txt">Table of n, a(n) for n = 0..200</a>
%H A132647 D. M. Jackson and R. C. Read, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002031183">A note on permutations without runs of given length</a>, Aequationes Math. 17 (1978), no. 2-3, 336-343.
%F A132647 G.f.: Sum_{n>=0} n!*((x^m-x)/(x^m-1))^n where m = 4.
%F A132647 a(n) ~ n! * (1 - 1/n^2 + 1/n^3 + 9/(2*n^4) + 7/n^5 - 55/(6*n^6) - 114/n^7 - 11419/(24*n^8) - 970/n^9 + 345199/(120*n^10) + ...). - _Vaclav Kotesovec_, Feb 17 2024
%o A132647 (PARI) seq(n)={Vec(sum(k=0, n, k!*((x^4-x)/(x^4-1) + O(x*x^n))^k))} \\ _Andrew Howroyd_, Aug 31 2018
%Y A132647 Cf. A000255, A002628.
%K A132647 nonn
%O A132647 0,3
%A A132647 Ivana Jovovic (ivana121(AT)EUnet.yu), Nov 14 2007
%E A132647 Terms a(16) and beyond from _Andrew Howroyd_, Aug 31 2018