%I #11 Sep 08 2022 08:46:09
%S 1,-3,-1,-2,-5,-14,-42,-132,-429,-1430,-4862,-16796,-58786,-208012,
%T -742900,-2674440,-9694845,-35357670,-129644790,-477638700,
%U -1767263190,-6564120420,-24466267020,-91482563640,-343059613650,-1289904147324,-4861946401452
%N Convolution inverse of A001700.
%H G. C. Greubel, <a href="/A246432/b246432.txt">Table of n, a(n) for n = 0..1660</a>
%F G.f.: (1 + sqrt(1 - 4*x)) / 2 - 2*x.
%F G.f.: -2*x + 1 - x / (1 - x / (1 - x / ...)) (continued fraction).
%F a(n) = A115140(n) = A115141(n) for all n in Z unless n=1.
%F a(n) = -A000108(n-1) for all n>1.
%e G.f. = 1 - 3*x - x^2 - 2*x^3 - 5*x^4 - 14*x^5 - 42*x^6 - 132*x^7 - 429*x^8 + ...
%t CoefficientList[Series[(1 +Sqrt[1-4*x])/2 -2*x, {x, 0, 50}], x] (* _G. C. Greubel_, Aug 04 2018 *)
%o (PARI) {a(n) = if( n<2, (n==0) - 3*(n==1), - binomial(2*n - 2, n-1) / n)};
%o (PARI) {a(n) = if( n<0, 0, polcoeff( (1 + sqrt(1 - 4*x + x * O(x^n))) / 2 - 2*x, n))};
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1 +Sqrt(1-4*x))/2 -2*x)); // _G. C. Greubel_, Aug 04 2018
%Y Cf. A000108, A001700, A115140, A115141.
%K sign
%O 0,2
%A _Michael Somos_, Nov 14 2014