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 A167635 #4 Jul 26 2022 10:39:01 %S A167635 1,0,1,0,2,0,5,1,14,7,43,36,143,166,509,731,1915,3158,7523,13560, %T A167635 30537,58257,127029,251266,538253,1089666,2313121,4754148,10051130, %U A167635 20868070,44065633,92132176,194617333,408971295,864899013,1824485600,3864369141 %N A167635 Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at odd level. %C A167635 a(n)=A167634(n,0). %F A167635 G.f.: G = [1 + 2z - z^3 - sqrt(1 - 4z^2 - 2z^3 + z^6)]/[2z(1 + z - z^2)]. %F A167635 D-finite with recurrence (n+1)*a(n) +a(n-1) +(-4*n+5)*a(n-2) +(-2*n+7)*a(n-3) +3*a(n-4) +a(n-5) +(n-6)*a(n-6)=0. - _R. J. Mathar_, Jul 26 2022 %e A167635 a(6)=5 because we have UUDDUUDDUUDD, UUDDUUUUDDDD, UUUUDDDDUUDD, UUUUDDUUDDDD, and UUUUUUDDDDDD. %p A167635 G := ((1+2*z-z^3-sqrt(1-4*z^2-2*z^3+z^6))*1/2)/(z*(1+z-z^2)): Gser := series(G, z = 0, 40): seq(coeff(Gser, z, n), n = 0 .. 38); %Y A167635 Cf. A167634, A167638 %K A167635 nonn %O A167635 0,5 %A A167635 _Emeric Deutsch_, Nov 08 2009