A382134 Number of completely asymmetric matchings (not containing centered or coupled arcs) of [2n].

1, 0, 0, 8, 48, 384, 4480, 59520, 897792, 15368192, 293769216, 6198589440, 143130972160, 3590253477888, 97214510235648, 2826205634330624, 87801981951344640, 2902989352269250560, 101776549707306237952, 3771425415371470405632, 147285455218020210180096

Offset: 0

Author

R. J. Mathar, Mar 17 2025

Keywords

• nonn

Links

• Sergi Elizalde and Emeric Deutsch, The degree of asymmetry of a sequence, Enum. Combinat. Applic. 2 (2022) no 1 #S2R7, theorem 5.1

Crossrefs

Cf. A000079, A001205, A047974, A053871.

Programs

Maple

g:= exp(-x-x^2)/sqrt(1-2*x) ;
seq( coeftayl(g,x=0,n)*n!,n=0..10) ;

Formula

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

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

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