%I #9 Aug 18 2018 11:23:58

%S 60,540,2160,6000,13500,26460,47040,77760,121500,181500,261360,365040,

%T 496860,661500,864000,1109760,1404540,1754460,2166000,2646000,3201660,

%U 3840540,4570560,5400000,6337500,7392060,8573040,9890160,11353500,12973500,14760960

%N Expansion of 60*x*(1 + 4*x + x^2) / (1 - x)^5.

%C Seems to be the negative of the second column of A316349.

%H Colin Barker, <a href="/A316458/b316458.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: 60*x*(1 + 4*x + x^2) / (1 - x)^5.

%F a(n) = 60 * A000537(n).

%F a(n) = 15*n^4 + 30*n^3 + 15*n^2.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%o (PARI) Vec(60*x*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))

%o (PARI) a(n) = 15*n^4 + 30*n^3 + 15*n^2

%Y Cf. A000537, A316349, A316457, A316459.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Aug 12 2018