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%I #37 Nov 04 2017 06:54:59
%S 1,0,-2,-3,0,7,11,1,-24,-40,-7,82,145,37,-279,-524,-174,945,1888,767,
%T -3185,-6783,-3244,10676,24301,13330,-35567,-86823,-53615,117672,
%U 309366,212101,-386224,-1099385,-827997,1255937,3896480,3197152,-4039199,-13773374
%N Row sums of number triangle A185962.
%H Vincenzo Librandi, <a href="/A185963/b185963.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,1).
%F G.f.: (1-x)^2/(1-2x+3x^2-x^3).
%F a(n) = Sum_{k=0..n} Sum_{i=0..(2k+2)} C(2k+2,i)*Sum_{j=0..(n-k-i)} C(k+j,j)*C(j,n-k-i-j)*(-1)^(n-k-j).
%F a(n) = Sum_{k=0..n} binomial(n+2k,3k)*(-1)^k = Sum_{k=0..n} A109955(n,k)*(-1)^k. - _Philippe Deléham_, Feb 18 2012
%F a(n) = A000931(-3*n). - _Michael Somos_, Sep 18 2012
%F a(n) = hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27). - _Peter Luschny_, Nov 03 2017
%e G.f. = 1 - 2*x^2 - 3*x^3 + 7*x^5 + 11*x^6 + x^7 - 24*x^8 - 40*x^9 + ...
%p a := n -> hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27):
%p seq(simplify(a(n)), n=0..39); # _Peter Luschny_, Nov 03 2017
%t LinearRecurrence[{2,-3,1},{1,0,-2},50] (* _Vincenzo Librandi_, Feb 18 2012 *)
%o (PARI) x='x+O('x^50); Vec((1-x)^2/(1-2*x+3*x^2-x^3)) \\ _G. C. Greubel_, Jul 23 2017
%Y Cf. A000931.
%K sign,easy
%O 0,3
%A _Paul Barry_, Feb 07 2011
%E More terms from _Philippe Deléham_, Feb 07 2012
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