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%I #10 Sep 08 2022 08:14:54
%S 84,1470,12936,77616,360360,1387386,4624620,13741728,37165128,
%T 92912820,217273056,479693760,1007356896,2024399916,3912705720,
%U 7303717344,13213962300,23241027810,39841761960,66720654000,109363854600,175763337750,277386503940,430459323840
%N a(n) = C(n+6,n)*C(n+9,6).
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: -((42*(x+1)*(x*(2*x+7)+2))/(x-1)^13). - _Harvey P. Dale_, Sep 14 2012
%F a(0)=84, a(1)=1470, a(2)=12936, a(3)=77616, a(4)=360360, a(5)=1387386, a(6)=4624620, a(7)=13741728, a(8)=37165128, a(9)=92912820, a(10)=217273056, a(11)=479693760, a(12)=1007356896, a(n)=13*a(n-1)- 78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)- 1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - _Harvey P. Dale_, Sep 14 2012
%F From _Amiram Eldar_, Sep 08 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 10446039/3920 - 270*Pi^2.
%F Sum_{n>=0} (-1)^n/a(n) = 82911/560 - 15*Pi^2. (End)
%e If n=0 then C(0+6,0)*C(0+9,6) = C(6,0)*C(9,6) = 1*84 = 84.
%e If n=6 then C(6+6,6)*C(6+9,6) = C(12,6)*C(15,6) = 924*5005 = 4624620.
%t Table[Binomial[n+6,n]Binomial[n+9,6],{n,0,30}] (* or *) CoefficientList[ Series[-((42 (x+1) (x (2 x+7)+2))/(x-1)^13),{x,0,30}],x] (* _Harvey P. Dale_, Sep 14 2012 *)
%Y Cf. A062145.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, Apr 27 2005
%E Corrected and extended by _Harvey P. Dale_, Sep 14 2012