%I #18 Sep 04 2022 04:06:49
%S 1,96,2808,43680,450450,3459456,21237216,109219968,486370170,
%T 1921462400,6859620768,22449667968,68128506264,193501082880,
%U 518306472000,1317650231040,3196331224515,7432299594720,16630917303000,35933837940000,75191555889450,152770145299200
%N a(n) = binomial(n+7,n)*binomial(n+11,n).
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).
%F G.f.: -(330*x^7+3234*x^6+9702*x^5+11550*x^4+5775*x^3+1155*x^2+77*x+1)/(x-1)^19. - _Colin Barker_, Jan 21 2013
%F From _Amiram Eldar_, Sep 04 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 308308*Pi^2/3 - 16431524791/16200.
%F Sum_{n>=0} (-1)^n/a(n) = 1232*Pi^2/3 + 360448*log(2)/45 - 108911693/11340. (End)
%e a(0): C(0+7,0)*C(0+11,0) = C(7,0)*C(11,0) = 1*1 = 1;
%e a(8): C(8+7,8)*C(8+11,8) = C(15,8)*(19,8) = 6435*75582 = 486370170.
%t f[n_] := Binomial[n + 7, n]Binomial[n + 11, n]; Table[ f[n], {n, 0, 19}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%o (Magma) [Binomial(n+7,n)*Binomial(n+11,n): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, Apr 14 2005
%E More terms from _Robert G. Wilson v_, Apr 20 2005
%E More terms from _Colin Barker_, Jan 21 2013