A382139 Number of matchings of [2n] with no coupled arcs.

1, 1, 1, 9, 81, 705, 7665, 100905, 1524705, 26022465, 496042785, 10445342985, 240779831985, 6030718158465, 163087008669585, 4735950860666025, 146987669673669825, 4855606200012593025, 170101350767940617025, 6298861062893921346825, 245834199405298416337425

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, eq (17) at r=1, s=2.

Crossrefs

Cf. A047974, A053871, A382134, A067994, A001147.

Programs

Maple

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

Formula

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

Exponential convolution of A067994 and A001147.

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