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 A370383 #19 Feb 19 2024 09:54:43
%S A370383 1,1,2,6,24,119,717,5026,40242,362376,3625081,39885851,478714416,
%T A370383 6224078292,87145277160,1307271652917,20917481850667,355612235468396,
%U A370383 6401234296266540,121626707638142280,2432586885636105251,51085230669413519349,1123891538655073251190
%N A370383 Number of permutations of [n] having no substring [k,k+1,k+2,k+3,k+4].
%H A370383 Alois P. Heinz, <a href="/A370383/b370383.txt">Table of n, a(n) for n = 0..450</a>
%H A370383 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 A370383 G.f.: Sum_{k>=0} k! * ( (x-x^5)/(1-x^5) )^k.
%F A370383 a(n) = Sum_{k=0..4} A184182(n,k). - _Alois P. Heinz_, Feb 17 2024
%o A370383 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*((x-x^5)/(1-x^5))^k))
%Y A370383 Cf. A000255, A002628, A132647, A184182, A370384.
%K A370383 nonn
%O A370383 0,3
%A A370383 _Seiichi Manyama_, Feb 17 2024