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A104673 a(n) = binomial(n+5, n)*binomial(n+10, n).

%I A104673 #18 Mar 02 2025 22:56:39
%S A104673 1,66,1386,16016,126126,756756,3699696,15402816,56316546,184940756,
%T A104673 554822268,1540663488,4001445448,9802357488,22805484768,50678855040,
%U A104673 108088495515,222161129190,441579528390,851355545040,1596291646950,2917485413700,5208073135200
%N A104673 a(n) = binomial(n+5, n)*binomial(n+10, n).
%H A104673 T. D. Noe, <a href="/A104673/b104673.txt">Table of n, a(n) for n = 0..1000</a>
%H A104673 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F A104673 G.f.: (1 + 50*x + 450*x^2 + 1200*x^3 + 1050*x^4 + 252*x^5)/(1-x)^16. - _Harvey P. Dale_, Nov 24 2011
%F A104673 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104673 Sum_{n>=0} 1/a(n) = 17875*Pi^2/3 - 7468753315/127008.
%F A104673 Sum_{n>=0} (-1)^n/a(n) = 208828891/127008 - 725*Pi^2/6 - 40960*log(2)/63. (End)
%e A104673 If n=0 then C(0+5,5)*C(0+10,0+0) = C(5,5)*C(10,0) = 1*1 = 1.
%e A104673 If n=6 then C(6+5,5)*C(6+10,6+0) = C(11,5)*C(16,6) = 462*8008 = 3699696.
%t A104673 Table[Binomial[n+5,5]Binomial[n+10,n],{n,0,30}]
%o A104673 (Magma)
%o A104673 A104673:= func< n | Binomial(n+5,n)*Binomial(n+10,n) >;
%o A104673 [A104673(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A104673 (SageMath)
%o A104673 def A104673(n): return binomial(n+5,n)*binomial(n+10,n)
%o A104673 print([A104673(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A104673 Cf. A062190.
%K A104673 easy,nonn
%O A104673 0,2
%A A104673 _Zerinvary Lajos_, Apr 22 2005
%E A104673 Corrected and extended by _Harvey P. Dale_, Nov 24 2011