%I #8 Aug 18 2018 11:24:25

%S 420,7140,41160,148680,411180,955500,1963920,3684240,6439860,10639860,

%T 16789080,25498200,37493820,53628540,74891040,102416160,137494980,

%U 181584900,236319720,303519720,385201740,483589260,601122480,740468400,904530900,1096460820

%N Expansion of 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.

%C Seems to be the negative of the third column of A316387.

%H Colin Barker, <a href="/A317983/b317983.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.

%F a(n) = 420 * A000538(n).

%F a(n) = 84*n^5 + 210*n^4 + 140*n^3 - 14*n.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%o (PARI) Vec(420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6 + O(x^40))

%o (PARI) a(n) = 84*n^5 + 210*n^4 + 140*n^3 - 14*n

%Y Cf. A000538, A316387, A317981, A317982, A317984.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Aug 13 2018