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 A270229 #22 Aug 04 2024 15:13:17
%S A270229 1,2,7,32,193,1382,11719,112604,1221889,14639786,192949639,2760749048,
%T A270229 42732172993,709490574158,12596398359367,237750425419508,
%U A270229 4757710386662401,100516614496518866,2236829315345704711,52262526676903613264,1279512810244450887361
%N A270229 Number of matchings in the 2 X n rook graph P_2 X K_n.
%C A270229 Sequence extended to n=0 using closed form. (binomial transform of A111883)
%H A270229 Andrew Howroyd, <a href="/A270229/b270229.txt">Table of n, a(n) for n = 0..50</a>
%F A270229 Binomial transform of A111883.
%F A270229 From _Vaclav Kotesovec_, Oct 01 2017: (Start)
%F A270229 a(n) = (n+1)*a(n-1) + (n-1)^2*a(n-2) - (n-2)*(n-1)^2*a(n-3) + (n-3)*(n-2)*(n-1)*a(n-4).
%F A270229 E.g.f.: exp((2-x)*x/(1-x)) / sqrt(1-x^2).
%F A270229 a(n) ~ exp(1/2 + 2*sqrt(n) - n) * n^n / 2.
%F A270229 (End)
%t A270229 a[n_] := Sum[Binomial[n, k]*Abs[HermiteH[k, I/Sqrt[2]]]^2/2^k, {k, 0, n}];
%t A270229 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Oct 01 2017 *)
%t A270229 CoefficientList[Series[E^((2-x)*x/(1-x)) / Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2017 *)
%Y A270229 Cf. A270227, A270228, A000085, A081919 (perfect matchings).
%K A270229 nonn
%O A270229 0,2
%A A270229 _Andrew Howroyd_, Mar 13 2016