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A104671 a(n) = binomial(n+3,n)*binomial(n+8,n).

%I A104671 #30 Mar 01 2025 16:45:47
%S A104671 1,36,450,3300,17325,72072,252252,772200,2123550,5348200,12514788,
%T A104671 27511848,57316350,113954400,217443600,400096224,712671399,1232995500,
%U A104671 2077825750,3418915500,5504453955,8687301480,13461727500,20510685000,30766027500,45484495056
%N A104671 a(n) = binomial(n+3,n)*binomial(n+8,n).
%H A104671 G. C. Greubel, <a href="/A104671/b104671.txt">Table of n, a(n) for n = 0..1000</a>
%H A104671 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A104671 G.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12. - _Bruno Berselli_, Jun 06 2012
%F A104671 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104671 Sum_{n>=0} 1/a(n) = 144*Pi^2 - 1739736/1225.
%F A104671 Sum_{n>=0} (-1)^n/a(n) = 16*Pi^2 - 13312*log(2)/35 - 515202/1225. (End)
%e A104671 If n=0 then C(0+3,3)*C(0+8,0+0) = C(3,3)*C(8,0) = 1*1 = 1.
%e A104671 If n=6 then C(6+3,3)*C(6+8,6+0) = C(9,3)*C(14,6) = 84*3003 = 252252.
%t A104671 Table[Binomial[n+3,3]Binomial[n+8,n],{n,0,30}] (* or *)
%t A104671 LinearRecurrence[ {12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,36,450,3300,17325,72072,252252,772200,2123550,5348200,12514788,27511848},30] (* _Harvey P. Dale_, Oct 05 2017 *)
%o A104671 (Magma)
%o A104671 A104671:= func< n | Binomial(n+3,n)*Binomial(n+8,n) >;
%o A104671 [A104671(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A104671 (SageMath)
%o A104671 def A104671(n): return binomial(n+3,n)*binomial(n+8,n)
%o A104671 print([A104671(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A104671 Cf. A062190.
%K A104671 nonn,easy
%O A104671 0,2
%A A104671 _Zerinvary Lajos_, Apr 22 2005
%E A104671 a(12) corrected by _Colin Barker_, Jun 06 2012
%E A104671 More terms and a(7), a(15) corrected by _Bruno Berselli_, Jun 06 2012