A294161 Column 1 of triangle A291844.

2, 23, 292, 4068, 62861, 1075562, 20275944, 418724047, 9418874022, 229535650138, 6029910590473, 169978358728536, 5120224516689050, 164192864744507615, 5585978669387706724, 200988595873323113508, 7626780547253339197109, 304431018444668653351250, 12752396616363975496913952, 559388848572350998030227895

Offset: 2

Author

Gheorghe Coserea, Nov 04 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 2..304

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(1))