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A107396 a(n) = binomial(n+5, 5) * binomial(n+7, 5).

%I A107396 #13 Feb 09 2025 03:41:50
%S A107396 21,336,2646,14112,58212,199584,594594,1585584,3864861,8744736,
%T A107396 18582564,37425024,71954064,132838272,236618172,408282336,684723501,
%U A107396 1119300336,1787771370,2795913120,4289184900,6464858400,9587091150,14005489680,20177780805,28697288256
%N A107396 a(n) = binomial(n+5, 5) * binomial(n+7, 5).
%H A107396 Andrew Howroyd, <a href="/A107396/b107396.txt">Table of n, a(n) for n = 0..1000</a>
%H A107396 <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 A107396 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A107396 Sum_{n>=0} 1/a(n) = 350*Pi^2/3 - 82901/72.
%F A107396 Sum_{n>=0} (-1)^n/a(n) = 1975/24 - 25*Pi^2/3. (End)
%F A107396 G.f.: 21*(1 + 5*x + 5*x^2 + x^3)/(1-x)^11. - _G. C. Greubel_, Feb 09 2025
%e A107396 If n=0 then C(0+5,5)*C(0+7,5) = C(5,5)*C(7,5) = 1*21 = 21.
%e A107396 If n=9 then C(6+5,5)*C(6+7,5) = C(11,5)*C(13,5) = 462*1287 = 594594.
%t A107396 a[n_] := Binomial[n + 5, 5] * Binomial[n + 7, 5]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)
%o A107396 (PARI) a(n)={binomial(n+5, 5) * binomial(n+7, 5)} \\ _Andrew Howroyd_, Nov 08 2019
%o A107396 (Magma)
%o A107396 A107396:= func< n | Binomial(n+5,5)*Binomial(n+7,5) >;
%o A107396 [A107396(n): n in [0..30]]; // _G. C. Greubel_, Feb 09 2025
%o A107396 (SageMath)
%o A107396 def A107396(n): return binomial(n+5,5)*binomial(n+7,5)
%o A107396 print([A107396(n) for n in range(31)]) # _G. C. Greubel_, Feb 09 2025
%Y A107396 Cf. A033987, A062196.
%K A107396 easy,nonn
%O A107396 0,1
%A A107396 _Zerinvary Lajos_, May 25 2005
%E A107396 a(7) corrected and terms a(15) and beyond from _Andrew Howroyd_, Nov 08 2019