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a(n) = n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4).
1

%I #18 Sep 08 2022 08:45:02

%S 0,8640,172800,1512000,8467200,35562240,121927680,359251200,940896000,

%T 2242468800,4947022080,10231341120,20033395200,37425024000,

%U 67118284800,116138603520,194702952960,317346724800,504348768000,783510235200

%N a(n) = n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4).

%H Robert Israel, <a href="/A057658/b057658.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).

%F From _Robert Israel_, Jun 06 2019: (Start)

%F G.f.: 8640*x*(x^4 + 10*x^3 + 20*x^2 + 10*x + 1)/(x - 1)^10.

%F (n + 3)*(n + 2)*a(n - 2) - 2*(n^2 + 2*n + 12)*a(n - 1) + n*(n - 1)*a(n) = 0. (End)

%F a(n) = 8640*A047819(n) for n > 0. - _Michel Marcus_, Jun 07 2019

%p seq(n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4), n=0..30); # _Robert Israel_, Jun 06 2019

%t Table[n (n+1)^2 (n+2)^3 (n+3)^2 (n+4), {n, 0, 40}] (* _Vincenzo Librandi_, Jun 07 2019 *)

%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,8640,172800,1512000,8467200,35562240,121927680,359251200,940896000,2242468800},30] (* _Harvey P. Dale_, Sep 24 2021 *)

%o (Magma) [n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4): n in [0..25]]; // _Vincenzo Librandi_, Jun 07 2019

%Y Cf. A047819.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 16 2000