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 A382134 #18 Mar 17 2025 16:01:46 %S A382134 1,0,0,8,48,384,4480,59520,897792,15368192,293769216,6198589440, %T A382134 143130972160,3590253477888,97214510235648,2826205634330624, %U A382134 87801981951344640,2902989352269250560,101776549707306237952,3771425415371470405632,147285455218020210180096 %N A382134 Number of completely asymmetric matchings (not containing centered or coupled arcs) of [2n]. %H A382134 Sergi Elizalde and Emeric Deutsch, <a href="https://doi.org/10.54550/ECA2022V2S1R7">The degree of asymmetry of a sequence</a>, Enum. Combinat. Applic. 2 (2022) no 1 #S2R7, theorem 5.1 %F A382134 E.g.f: exp(-x-x^2)/sqrt(1-2*x). %F A382134 a(n) = 2^n * A001205(n). %F A382134 D-finite with recurrence a(n) +2*(-n+1)*a(n-1) -4*(n-1)*(n-2)*a(n-3)=0. %p A382134 g:= exp(-x-x^2)/sqrt(1-2*x) ; %p A382134 seq( coeftayl(g,x=0,n)*n!,n=0..10) ; %Y A382134 Cf. A000079, A001205, A047974, A053871. %K A382134 nonn %O A382134 0,4 %A A382134 _R. J. Mathar_, Mar 17 2025