cp's OEIS Frontend

A294160 Column 0 of triangle A291844.

%I A294160 #6 Nov 12 2017 06:13:19
%S A294160 1,1,4,29,274,3145,42294,651227,11295242,217954807,4632600152,
%T A294160 107572674851,2710093290348,73635362430373,2146667383237600,
%U A294160 66842659455306545,2214207331808233390,77752904712525291757,2885163506590219810722,112808263228714108970879
%N A294160 Column 0 of triangle A291844.
%o A294160 (PARI)
%o A294160 A291843_ser(N, t='t) = {
%o A294160   my(x='x+O('x^N), y=1, y1=0, n=1,
%o A294160   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 A294160   while (n++,
%o A294160    y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
%o A294160         (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
%o A294160    if (y1 == y, break); y = y1; ); y;
%o A294160 };
%o A294160 A291844_ser(N, t='t) = {
%o A294160   my(z = A291843_ser(N+1, t));
%o A294160   ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
%o A294160 };
%o A294160 A291844_kol(k, N=20) = {
%o A294160   my(s = A291844_ser(N+1+3*k\2, t='t + O('t^(k+1))));
%o A294160   Ser(polcoeff(s, k,'t), 'x, N);
%o A294160 };
%o A294160 Vec(A291844_kol(0))
%Y A294160 Cf. A291844.
%K A294160 nonn
%O A294160 0,3
%A A294160 _Gheorghe Coserea_, Nov 03 2017