%I #9 Sep 01 2022 07:13:42
%S 21,336,2646,14112,58212,199584,594594,1585584,3864861,8744736,
%T 18582564,37425024,71954064,132838272,236618172,408282336,684723501,
%U 1119300336,1787771370,2795913120,4289184900,6464858400,9587091150,14005489680,20177780805,28697288256
%N a(n) = binomial(n+5, 5) * binomial(n+7, 5).
%H Andrew Howroyd, <a href="/A107396/b107396.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 From _Amiram Eldar_, Sep 01 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 350*Pi^2/3 - 82901/72.
%F Sum_{n>=0} (-1)^n/a(n) = 1975/24 - 25*Pi^2/3. (End)
%e If n=0 then C(0+5,5)*C(0+7,5) = C(5,5)*C(7,5) = 1*21 = 21.
%e If n=9 then C(6+5,5)*C(6+7,5) = C(11,5)*C(13,5) = 462*1287 = 594594.
%t a[n_] := Binomial[n + 5, 5] * Binomial[n + 7, 5]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)
%o (PARI) a(n)={binomial(n+5, 5) * binomial(n+7, 5)} \\ _Andrew Howroyd_, Nov 08 2019
%Y Cf. A062196.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, May 25 2005
%E a(7) corrected and terms a(15) and beyond from _Andrew Howroyd_, Nov 08 2019