A294166 Row sums of A291843.

1, 0, 1, 8, 71, 789, 10365, 157031, 2692497, 51519756, 1088093185, 25140587651, 630820490833, 17082650998878, 496596665961713, 15425333714935513, 509890407550644949, 17871584701588777344, 662057571007292023593, 25847670560115633381442

Offset: 0

Author

Gheorghe Coserea, Nov 05 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..303

Crossrefs

Cf. A291843.

Programs

PARI

A291843_ser(N, t='t) = {
  my(x='x+O('x^N), y=1, y1=0, n=1,
  dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));
  while (n++,
   y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
        (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
   if (y1 == y, break); y = y1; ); y;
};
Vec(A291843_ser(20,1))

Formula

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).