A294167 - OEIS

%I #11 Nov 12 2017 06:10:33

%S 3,33,388,5101,75444,1248911,22964112,465344235,10316541393,

%T 248583207948,6472094085480,181133509590584,5424172954377851,

%U 173089061380034193,5864328868997378224,210259284591708083349,7954221480382049449284,316654854011156144727459,13233287747652092826502116

%N Column 1 of triangle A291843.

%H Gheorghe Coserea, <a href="/A294167/b294167.txt">Table of n, a(n) for n = 3..305</a>

%o (PARI)

%o A291843_ser(N, t='t) = {

%o   my(x='x+O('x^N), y=1, y1=0, n=1,

%o   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   while (n++,

%o    y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +

%o         (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;

%o    if (y1 == y, break); y = y1; ); y;

%o };

%o A291843_kol(k, N=19) = {

%o   my(s = A291843_ser(N+1+3*(k+1)\2, t='t + O('t^(k+1))));

%o   Ser(polcoeff(s, k, 't), 'x, N);

%o };

%o Vec(A291843_kol(1))

%Y Cf. A291843.

%K nonn

%O 3,1

%A _Gheorghe Coserea_, Nov 06 2017