cp's OEIS Frontend

A294161 Column 1 of triangle A291844.

%I A294161 #7 Nov 12 2017 06:12:50
%S A294161 2,23,292,4068,62861,1075562,20275944,418724047,9418874022,
%T A294161 229535650138,6029910590473,169978358728536,5120224516689050,
%U A294161 164192864744507615,5585978669387706724,200988595873323113508,7626780547253339197109,304431018444668653351250,12752396616363975496913952,559388848572350998030227895
%N A294161 Column 1 of triangle A291844.
%H A294161 Gheorghe Coserea, <a href="/A294161/b294161.txt">Table of n, a(n) for n = 2..304</a>
%o A294161 (PARI)
%o A294161 A291843_ser(N, t='t) = {
%o A294161   my(x='x+O('x^N), y=1, y1=0, n=1,
%o A294161   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 A294161   while (n++,
%o A294161    y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
%o A294161         (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
%o A294161    if (y1 == y, break); y = y1; ); y;
%o A294161 };
%o A294161 A291844_ser(N, t='t) = {
%o A294161   my(z = A291843_ser(N+1, t));
%o A294161   ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
%o A294161 };
%o A294161 A291844_kol(k, N=20) = {
%o A294161   my(s = A291844_ser(N+1+3*k\2, t='t + O('t^(k+1))));
%o A294161   Ser(polcoeff(s, k,'t), 'x, N);
%o A294161 };
%o A294161 Vec(A291844_kol(1))
%Y A294161 Cf. A291844.
%K A294161 nonn
%O A294161 2,1
%A A294161 _Gheorghe Coserea_, Nov 04 2017