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A107397 a(n) = binomial(n+6, 6) * binomial(n+8, 6).

%I A107397 #13 Feb 12 2025 14:22:28
%S A107397 28,588,5880,38808,194040,792792,2774772,8588580,24048024,61941880,
%T A107397 148660512,335785632,719540640,1472290848,2891999880,5477788008,
%U A107397 10042611348,17877713700,30988037080,52423371000,86736850200,140610670200,223698793500,349748200620,538074154800
%N A107397 a(n) = binomial(n+6, 6) * binomial(n+8, 6).
%H A107397 Andrew Howroyd, <a href="/A107397/b107397.txt">Table of n, a(n) for n = 0..1000</a>
%H A107397 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A107397 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A107397 Sum_{n>=0} 1/a(n) = 720*Pi^2 - 1740989/245.
%F A107397 Sum_{n>=0} (-1)^n/a(n) = 6144*log(2)/7 - 149046/245. (End)
%F A107397 G.f.: 28*(1 + 8*x + 15*x^2 + 8*x^3 + x^4)/(1-x)^13. - _G. C. Greubel_, Feb 09 2025
%e A107397 If n=0 then C(0+6,6)*C(0+8,6) = C(6,6)*C(8,6) = 1*28 = 28.
%e A107397 If n=6 then C(6+6,6)*C(6+8,6) = C(12,6)*C(14,6) = 924*3003 = 2774772.
%t A107397 a[n_] := Binomial[n + 6, 6] * Binomial[n + 8, 6]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)
%o A107397 (PARI) a(n)={binomial(n+6, 6) * binomial(n+8, 6)} \\ _Andrew Howroyd_, Nov 08 2019
%o A107397 (Magma)
%o A107397 A107397:= func< n | Binomial(n+6,6)*Binomial(n+8,6) >;
%o A107397 [A107397(n): n in [0..30]]; // _G. C. Greubel_, Feb 09 2025
%o A107397 (SageMath)
%o A107397 def A107397(n): return binomial(n+6,6)*binomial(n+8,6)
%o A107397 print([A107397(n) for n in range(31)]) # _G. C. Greubel_, Feb 09 2025
%Y A107397 Cf. A033987, A062196.
%K A107397 easy,nonn
%O A107397 0,1
%A A107397 _Zerinvary Lajos_, May 25 2005
%E A107397 a(3) corrected and terms a(11) and beyond from _Andrew Howroyd_, Nov 08 2019