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%I #11 Feb 15 2014 02:30:57
%S 1,-1,2,-6,22,-90,394,-1806,8558,-41586,206098,-1037718,5293446,
%T -27297738,142078746,-745387038,3937603038,-20927156706,111818026018,
%U -600318853926,3236724317174,-17518619320890,95149655201962,-518431875418926,2832923350929742,-15521467648875090
%N First column of inverse of Delannoy triangle.
%C First column of A103136. The positive sequence has g.f. 1+xS(x). It is the first column of the inverse of the signed Delannoy triangle which has general term T(n,k)=if(k<=n, sum{j=0..k, 2^j*C(n-k,j)C(k,j)}(-1)^(n-k),0).
%H Vincenzo Librandi, <a href="/A103137/b103137.txt">Table of n, a(n) for n = 0..200</a>
%F G.f.: 1-xS(-x), where S(x) is the g.f. of the large Schroeder numbers A006318.
%F Conjecture: n*a(n) +3*(2*n-3)*a(n-1) +(n-3)*a(n-2)=0. - _R. J. Mathar_, Nov 26 2012
%F a(n) ~ (-1)^n * sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Feb 13 2014
%t CoefficientList[Series[1+x*(1+x-(1+6*x+x^2)^(1/2))/(2*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 13 2014 *)
%Y A minor variation of A006318.
%K easy,sign
%O 0,3
%A _Paul Barry_, Jan 24 2005
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