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A103604 a(n) = binomial(n+6,6) * binomial(n+10,6).

%I A103604 #24 Mar 05 2025 01:48:55
%S A103604 210,3234,25872,144144,630630,2312310,7399392,21237216,55747692,
%T A103604 135795660,310390080,671571264,1385115732,2738894004,5216940960,
%U A103604 9610154400,17178150990,29881321470,50707697040,84126042000,136704818250,217946538810,341398774080,526116951360
%N A103604 a(n) = binomial(n+6,6) * binomial(n+10,6).
%H A103604 T. D. Noe, <a href="/A103604/b103604.txt">Table of n, a(n) for n = 0..1000</a>
%H A103604 <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 A103604 G.f.: 42*(5+12*x+5*x^2) / (1-x)^13. - _Colin Barker_, Jul 01 2015
%F A103604 a(n) = A000579(n+6)*A000579(n+10). - _Michel Marcus_, Jul 01 2015
%F A103604 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A103604 Sum_{n>=0} 1/a(n) = 60*Pi^2 - 10445899/17640.
%F A103604 Sum_{n>=0} (-1)^n/a(n) = 447173/2205 - 2048*log(2)/7. (End)
%t A103604 Table[Binomial[n+6,6]Binomial[n+10,6],{n,0,30}] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{210,3234,25872, 144144,630630,2312310,7399392,21237216,55747692,135795660,310390080, 671571264,1385115732},30] (* _Harvey P. Dale_, Apr 18 2019 *)
%o A103604 (PARI) a(n) = binomial(n+6,6)*binomial(n+10,6) \\ _Colin Barker_, Jul 01 2015
%o A103604 (PARI) Vec(-42*(5*x^2+12*x+5)/(x-1)^13 + O(x^30)) \\ _Colin Barker_, Jul 01 2015
%o A103604 (Magma)
%o A103604 A103604:= func< n | Binomial(n+6,6)*Binomial(n+10,6) >;
%o A103604 [A103604(n): n in [0..30]]; // _G. C. Greubel_, Mar 05 2025
%o A103604 (SageMath)
%o A103604 def A103604(n): return binomial(n+6,6)*binomial(n+10,6)
%o A103604 print([A103604(n) for n in range(31)]) # _G. C. Greubel_, Mar 05 2025
%Y A103604 Cf. A000579, A062264.
%K A103604 nonn,easy
%O A103604 0,1
%A A103604 _Zerinvary Lajos_, Apr 22 2005