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%I #13 Jul 20 2021 07:02:50
%S 1,1,5,17,73,321,1485,7073,34513,171585,866133,4427313,22870425,
%T 119208321,626178717,3311424321,17615732385,94202293633,506116560293,
%U 2730607756881,14788011564009,80361643637953,438070231780973
%N Alternating sum of large Schroeder numbers.
%C Hankel transform is A166231. Binomial transform is A166229.
%H Vincenzo Librandi, <a href="/A166228/b166228.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: (1-x-sqrt(1-6x+x^2))/(2x(1+x));
%F a(n) = Sum{k=0..n} (-1)^k*A006318(n-k) = Sum_{k=0..n} (-1)^(n-k)*A006318(k).
%F Conjecture: (n+1)*a(n) +(4-5n)*a(n-1) +(1-5n)*a(n-2) +(n-2)*a(n-3)=0. - _R. J. Mathar_, Nov 17 2011
%F a(n) ~ sqrt(48+34*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 20 2012
%t CoefficientList[Series[(1-x-Sqrt[1-6*x+x^2])/(2*x*(1+x)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 20 2012 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 09 2009