|
%I #9 Sep 08 2022 06:37:31
%S 1,63,1260,13860,103950,594594,2774772,11042460,38648610,121671550,
%T 350414064,935402832,2338507080,5521090680,12394285200,26606398896,
%U 54875697723,109181751525,210275965900,393175282500,715579014150,1270517841450,2205030964500,3747302149500
%N a(n) = C(n+8,8)*C(n+6,6).
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F From _Amiram Eldar_, Sep 08 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 6336*Pi^2 - 76602676/1225.
%F Sum_{n>=0} (-1)^n/a(n) = 1365906/1225 - 80*Pi^2 - 16384*log(2)/35. (End)
%e If n=0 then C(0+8,8)*C(0+6,6) = C(8,8)*C(6,6) = 1*1 = 1.
%e If n=6 then C(6+8,8)*C(6+6,6) = C(14,8)*C(12,6) = 3003*924 = 2774772.
%t Table[Binomial[n+8,8]Binomial[n+6,6],{n,0,20}] (* _Harvey P. Dale_, Sep 02 2016 *)
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 21 2005
%E More terms from _Harvey P. Dale_, Sep 02 2016
|
