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

0,4

Links

Table of n, a(n) for n=0..20.

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.

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.

a(n) ~ 2^(n + 1/2) * n^n / exp(n + 1/4). - Vaclav Kotesovec, Apr 30 2026

Maple

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

Crossrefs

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

Sequence in context: A206857 A073531 A206694 * A125910 A171283 A383201

Adjacent sequences: A382136 A382137 A382138 * A382140 A382141 A382142

Keyword

nonn

Author

R. J. Mathar, Mar 17 2025

Status

approved