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%I #29 Jan 31 2022 09:01:08
%S 1,2,5,17,67,322,1729,10745,72989,556514,4570909,41300833,397831735,
%T 4156207538,45928539713,544673444273,6790954845241,90125991819010,
%U 1251379270355221,18375317715967121,281164964490563531,4525863356878968482
%N a(1)=1; a(2)=2; for n>2, a(n)=a(n-1)+A000217(n-1)*a(n-2).
%C Equals the eigensequence of an infinite lower triangular matrix with 1's in the main diagonal and the triangular series in the subdiagonal.
%H Reinhard Zumkeller, <a href="/A166474/b166474.txt">Table of n, a(n) for n = 1..250</a>
%F a(n+1) = A166469(A066120(n)).
%F E.g.f.: -2*exp(sqrt(2)*arctanh(x/sqrt(2)))/(x^2-2) = ((sqrt(2) + x)^2/(2 - x^2))^(1/sqrt(2))*2/(2 - x^2). - _Vaclav Kotesovec_, Oct 19 2012
%F a(n) ~ n!*2^(1/sqrt(2)-n/2)*n^(1/sqrt(2))/(2*Gamma(1+1/sqrt(2))). - _Vaclav Kotesovec_, Oct 19 2012
%t Rest[CoefficientList[Series[-2*E^(Sqrt[2]*ArcTanh[x/Sqrt[2]])/(x^2-2), {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%o (Haskell)
%o a166474 n = a166474_list !! (n-1)
%o a166474_list = 1 : 2 : zipWith (+)
%o (tail a166474_list) (zipWith (*) a166474_list $ drop 2 a000217_list)
%o -- _Reinhard Zumkeller_, Feb 27 2012
%Y Cf. A166469, A066120, A351046.
%K nonn
%O 1,2
%A _Matthew Vandermast_, Nov 05 2009
%E More terms from _Sean A. Irvine_, Jun 16 2011
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