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 A382139 #8 Mar 17 2025 14:23:42 %S A382139 1,1,1,9,81,705,7665,100905,1524705,26022465,496042785,10445342985, %T A382139 240779831985,6030718158465,163087008669585,4735950860666025, %U A382139 146987669673669825,4855606200012593025,170101350767940617025,6298861062893921346825,245834199405298416337425 %N A382139 Number of matchings of [2n] with no coupled arcs. %H A382139 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, eq (17) at r=1, s=2. %F A382139 E.g.f: exp(-x^2)/sqrt(1-2*x). %F A382139 Exponential convolution of A067994 and A001147. %F A382139 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. %p A382139 g:= exp(-x^2)/sqrt(1-2*x) ; %p A382139 seq( coeftayl(g,x=0,n)*n!,n=0..10) ; %Y A382139 Cf. A047974, A053871, A382134, A067994, A001147. %K A382139 nonn %O A382139 0,4 %A A382139 _R. J. Mathar_, Mar 17 2025