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%I #20 Apr 03 2023 09:16:45
%S 1,2,4,10,28,86,284,998,3700,14386,58372,246218,1076156,4860710,
%T 22635292,108459814,533813716,2694524642,13930068740,73667056394,
%U 398075350108,2195824771702,12353156545564,70818633296870
%N a(n) = 2*a(n-1) + (n-2)*a(n-2) with a(0) = 1, a(1) = 2.
%H Vincenzo Librandi, <a href="/A027412/b027412.txt">Table of n, a(n) for n = 0..200</a>
%H R. Donaghey, <a href="http://dx.doi.org/10.1016/0097-3165(76)90060-1">Binomial self-inverse sequences and tangent coefficients</a>, J. Combin. Theory, Series A, 21 (1976), 155-163.
%F a(n) = 2 * A005425(n-1), n > 0.
%F a(n) ~ sqrt(2)*exp(2*sqrt(n)-n/2-1)*n^(n/2-1/2). - _Vaclav Kotesovec_, Oct 08 2012
%t RecurrenceTable[{a[0]==1, a[1]==2, a[n]==2 a[n-1] + (n-2) a[n-2]}, a,{ n, 40}] (* _Vincenzo Librandi_, Dec 29 2012 *)
%t Table[If[n==0, 1, 2*(-I/Sqrt[2])^(n-1)*HermiteH[n-1, I*Sqrt[2]]], {n, 0, 40}] (* _G. C. Greubel_, Apr 01 2023 *)
%o (Magma) [n le 2 select n else 2*Self(n-1) + (n-3)*Self(n-2): n in [1..40]]; // _G. C. Greubel_, Apr 01 2023
%o (SageMath) [1]+[2*(-i/sqrt(2))^(n-1)*hermite(n-1, i*sqrt(2)) for n in range(1,41)] # _G. C. Greubel_, Apr 01 2023
%Y Cf. A005425.
%K nonn,easy
%O 0,2
%A _Olivier Gérard_
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