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%I #16 Jan 22 2020 02:21:50
%S 1,-1,3,-13,67,-381,2307,-14589,95235,-636925,4341763,-30056445,
%T 210731011,-1493303293,10678370307,-76957679613,558403682307,
%U -4075996839933,29909606989827,-220510631755773,1632599134961667,-12133359132082173,90485602494971907,-676925762716041213
%N Expansion of 1/(1+x*c(-2*x)), c(x) the g.f. of A000108.
%C First column of A114189. Row sums of A114193. Alternating sign version of A062992.
%H Vincenzo Librandi, <a href="/A114191/b114191.txt">Table of n, a(n) for n = 0..200</a>
%F G.f.: 4/(3+sqrt(1+8*x)).
%F a(n) = Sum_{k=0..n} (-2)^(n-k)*A039599(n, k) = Sum_{k=0..n} (-2)^(n-k)*C(2*n, n-k)*(2*k+1)/(n+k+1). - _Philippe Deléham_, Nov 17 2005
%F Conjecture: n*a(n) + (7*n-12)*a(n-1) + 4*(3-2*n)*a(n-2) = 0. - _R. J. Mathar_, Nov 14 2011
%F a(n) ~ (-1)^n * 2^(3*n+1) / (9 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 12 2014
%t CoefficientList[Series[4/(3+Sqrt[1+8*x]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 12 2014 *)
%K easy,sign
%O 0,3
%A _Paul Barry_, Nov 16 2005
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