A382134 - OEIS

%I #18 Mar 17 2025 16:01:46

%S 1,0,0,8,48,384,4480,59520,897792,15368192,293769216,6198589440,

%T 143130972160,3590253477888,97214510235648,2826205634330624,

%U 87801981951344640,2902989352269250560,101776549707306237952,3771425415371470405632,147285455218020210180096

%N Number of completely asymmetric matchings (not containing centered or coupled arcs) of [2n].

%H 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 E.g.f: exp(-x-x^2)/sqrt(1-2*x).

%F a(n) = 2^n * A001205(n).

%F D-finite with recurrence a(n) +2*(-n+1)*a(n-1) -4*(n-1)*(n-2)*a(n-3)=0.

%p g:= exp(-x-x^2)/sqrt(1-2*x) ;

%p seq( coeftayl(g,x=0,n)*n!,n=0..10) ;

%Y Cf. A000079, A001205, A047974, A053871.

%K nonn

%O 0,4

%A _R. J. Mathar_, Mar 17 2025