I've been struggling with a differential equation in one variable with variable coefficients. Neither Maple nor Mma could solve it, and indeed there may well be no closed form solution. But if there IS I would like to know about it, so I'm asking if anyone here can solve it. Let A(x) = Sum_{n>=0} a(n)*x^n/n! = 1 + 3*x + 31*x^2/2! + 45296*x^3/3! + 4061871*x^4/4! + ... be the exponential generating function for the sequence A144416. This sequence satisfies a complicated recurrence: Define U1:=n->(9/2)*n^2+(63/2)*n+105/2; U2:=n->(9/2)*n^2+24*n+34; U3:=n->6*n+23/2; U4:=n->5/2; then a(n+4)-U1(n)*a(n+3)-U2(n)*a(n+2)-U3(n)*a(n+1)-U4(n)*a(n) = 0 for n >= 0. Let Ai be shorthand for the i-th deriv of A(x) wrt x. Then the recurrence becomes the differential equation: A4 = ((9/2)*x^2*A5+36*x*A4+(105/2)*A3) + ((9/2)*x^2*A4+(57/2)*x*A3+34*A2) + (6*x*A2+(23/2)*A1) + (5/2)*A , with initial conditions A(0)=1, A'(0)=3, A''(0)=31, A'''(0)=842, A''''(0)=45296. It's unlikely, but can this be solved, e.g. in terms of hypergeometric functions? Neil