Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #25 Aug 30 2022 09:44:25
%S 252,2772,16632,72072,252252,756756,2018016,4900896,11027016,23279256,
%T 46558512,88884432,162954792,288304632,494236512,823727520,1338557220,
%U 2125943820,3307023720,5047562520,7571343780,11176745580,16257084480,23325382080,33044291280
%N a(n) = C(n+5,5)*C(n+10,5).
%H Colin Barker, <a href="/A104679/b104679.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.: 252 / (1-x)^11. - _Colin Barker_, Feb 07 2015
%F a(n) = A000389(n+5)*A000389(n+10) = 252*A001287(n+11). - _R. J. Mathar_, Nov 29 2015
%F From _Amiram Eldar_, Aug 30 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 5/1134.
%F Sum_{n>=0} (-1)^n/a(n) = 1280*log(2)/63 - 447047/31752. (End)
%e If n=0 then C(0+5,0+0)*C(0+10,5) = C(5,0)*C(10,5) = 1*252 = 252.
%e If n=4 then C(4+5,4+0)*C(4+10,5) = C(9,4)*C(14,5) = 126*2002 = 252252.
%t Table[Binomial[n+5,n]Binomial[n+10,5],{n,0,20}] (* _Harvey P. Dale_, Feb 06 2015 *)
%o (PARI) Vec(252/(1-x)^11 + O(x^100)) \\ _Colin Barker_, Feb 07 2015
%o (Magma) [Binomial(n+5,n)*Binomial(n+10,5): n in [0..30]]; // _G. C. Greubel_, Nov 25 2017
%Y Cf. A062190.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, Apr 22 2005
%E Corrected and extended by _Harvey P. Dale_, Feb 06 2015