%I #16 Mar 19 2024 08:31:11
%S 48,175,1680,25410,294000,2295513,12991440,57550100,211281840,
%T 669529875,1885734928,4823347830,11387316720,25126129245,52326450000,
%U 103659864168,196585724720,358766207415,632810010000,1082730294250,1802581066608,2927824829985,4650083620560
%N a(n) = 4*(n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*(n^4 + 4!)/4!.
%H T. D. Noe, <a href="/A131683/b131683.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: -(80*x^9 +7205*x^8 +61625*x^7 +213873*x^6 +217437*x^5 +93855*x^4 +8635*x^3 +2395*x^2 -353*x +48) / (x -1)^11. - _Colin Barker_, Aug 08 2013
%F a(0)=48, a(1)=175, a(2)=1680, a(3)=25410, a(4)=294000, a(5)=2295513, a(6)=12991440, a(7)=57550100, a(8)=211281840, a(9)=669529875, a(10)=1885734928, a(n)=11*a(n-1)- 55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)- 165*a(n-8)+ 55*a(n-9)- 11*a(n-10)+a(n-11). - _Harvey P. Dale_, Mar 23 2015
%t Table[((n+1)(n^2+2)(n^3+6)(n^4+24))/6,{n,0,30}] (* or *) LinearRecurrence[ {11,-55,165,-330,462,-462,330,-165,55,-11,1},{48,175,1680,25410,294000,2295513,12991440,57550100,211281840,669529875,1885734928},30] (* _Harvey P. Dale_, Mar 23 2015 *)
%Y See A049614.
%K nonn,easy
%O 0,1
%A _Alexander R. Povolotsky_, Aug 29 2007