A294160 Column 0 of triangle A291844.

1, 1, 4, 29, 274, 3145, 42294, 651227, 11295242, 217954807, 4632600152, 107572674851, 2710093290348, 73635362430373, 2146667383237600, 66842659455306545, 2214207331808233390, 77752904712525291757, 2885163506590219810722, 112808263228714108970879

Offset: 0

Author

Gheorghe Coserea, Nov 03 2017

Keywords

• nonn

Crossrefs

Cf. A291844.

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;
};
A291844_ser(N, t='t) = {
  my(z = A291843_ser(N+1, t));
  ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
};
A291844_kol(k, N=20) = {
  my(s = A291844_ser(N+1+3*k\2, t='t + O('t^(k+1))));
  Ser(polcoeff(s, k,'t), 'x, N);
};
Vec(A291844_kol(0))