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Column 0 of triangle A291844.
5

%I #6 Nov 12 2017 06:13:19

%S 1,1,4,29,274,3145,42294,651227,11295242,217954807,4632600152,

%T 107572674851,2710093290348,73635362430373,2146667383237600,

%U 66842659455306545,2214207331808233390,77752904712525291757,2885163506590219810722,112808263228714108970879

%N Column 0 of triangle A291844.

%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 A291844_ser(N, t='t) = {

%o my(z = A291843_ser(N+1, t));

%o ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);

%o };

%o A291844_kol(k, N=20) = {

%o my(s = A291844_ser(N+1+3*k\2, t='t + O('t^(k+1))));

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

%o };

%o Vec(A291844_kol(0))

%Y Cf. A291844.

%K nonn

%O 0,3

%A _Gheorghe Coserea_, Nov 03 2017