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A104672 a(n) = binomial(n+4,n)*binomial(n+9,n).

%I A104672 #14 Mar 02 2025 08:00:58
%S A104672 1,50,825,7700,50050,252252,1051050,3775200,12033450,34763300,
%T A104672 92470378,229265400,534952600,1183859600,2500601400,5067885504,
%U A104672 9898213875,18700431750,34284124875,61160599500,106419443130,180985447500,301393121250,492256440000,789661372500
%N A104672 a(n) = binomial(n+4,n)*binomial(n+9,n).
%H A104672 G. C. Greubel, <a href="/A104672/b104672.txt">Table of n, a(n) for n = 0..1000</a>
%H A104672 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A104672 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104672 Sum_{n>=0} 1/a(n) = 990*Pi^2 - 38297957/3920.
%F A104672 Sum_{n>=0} (-1)^n/a(n) = 15*Pi^2 - 12288*log(2)/7 + 4193253/3920. (End)
%F A104672 G.f.: (1 + 36*x + 216*x^2 + 336*x^3 + 126*x^4)/(1-x)^14. - _G. C. Greubel_, Mar 01 2025
%e A104672 If n=0 then C(0+4,4)*C(0+9,0+0) = C(4,4)*C(9,0) = 1*1 = 1.
%e A104672 If n=6 then C(6+4,4)*C(6+9,6+0) = C(10,4)*C(15,6) = 210*5005 = 1051050.
%t A104672 Table[Binomial[n+4,4]Binomial[n+9,n],{n,0,20}] (* _Harvey P. Dale_, Nov 15 2018 *)
%o A104672 (Magma)
%o A104672 A104672:= func< n | Binomial(n+4,n)*Binomial(n+9,n) >;
%o A104672 [A104672(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A104672 (SageMath)
%o A104672 def A104672(n): return binomial(n+4,n)*binomial(n+9,n)
%o A104672 print([A104672(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A104672 Cf. A062190.
%K A104672 easy,nonn
%O A104672 0,2
%A A104672 _Zerinvary Lajos_, Apr 22 2005
%E A104672 More terms from _Harvey P. Dale_, Nov 15 2018