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A294166 Row sums of A291843.

%I A294166 #8 Nov 12 2017 06:11:10
%S A294166 1,0,1,8,71,789,10365,157031,2692497,51519756,1088093185,25140587651,
%T A294166 630820490833,17082650998878,496596665961713,15425333714935513,
%U A294166 509890407550644949,17871584701588777344,662057571007292023593,25847670560115633381442
%N A294166 Row sums of A291843.
%H A294166 Gheorghe Coserea, <a href="/A294166/b294166.txt">Table of n, a(n) for n = 0..303</a>
%F A294166 G.f. y(x) satisfies: 0 = 2*x^2*(1+x)*y*deriv(y,x) + x*y^2 - (1+x)^2*(1-2*x)*y + (1+x)*(1-2*x).
%o A294166 (PARI)
%o A294166 A291843_ser(N, t='t) = {
%o A294166   my(x='x+O('x^N), y=1, y1=0, n=1,
%o A294166   dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));
%o A294166   while (n++,
%o A294166    y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
%o A294166         (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
%o A294166    if (y1 == y, break); y = y1; ); y;
%o A294166 };
%o A294166 Vec(A291843_ser(20,1))
%Y A294166 Cf. A291843.
%K A294166 nonn
%O A294166 0,4
%A A294166 _Gheorghe Coserea_, Nov 05 2017