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A105944 a(n) = binomial(n+8,n)*binomial(n+11,8).

%I A105944 #20 Mar 12 2025 04:45:33
%S A105944 165,4455,57915,495495,3185325,16563690,73002930,281582730,972740340,
%T A105944 3062330700,8904315420,24168856140,61764854580,149660993790,
%U A105944 345855237750,766005304350,1632800780325,3361648665375,6705510829875,12993932469375,24518985616125
%N A105944 a(n) = binomial(n+8,n)*binomial(n+11,8).
%H A105944 G. C. Greubel, <a href="/A105944/b105944.txt">Table of n, a(n) for n = 0..1000</a>
%H A105944 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F A105944 G.f.: 165*(1+x)*(1+9*x+19*x^2+9*x^3+x^4)/(1-x)^17. - _Colin Barker_, Jan 28 2013
%F A105944 From _Amiram Eldar_, Sep 08 2022: (Start)
%F A105944 Sum_{n>=0} 1/a(n) = 1493776559/14175 - 32032*Pi^2/3.
%F A105944 Sum_{n>=0} (-1)^n/a(n) = 112*Pi^2 - 1740989/1575. (End)
%F A105944 a(n) = 165*A030648(n). - _G. C. Greubel_, Mar 10 2025
%e A105944 If n=0 then C(0+8,0)*C(0+11,8) = C(8,0)*C(11,8) = 1*165 = 165.
%e A105944 If n=4 then C(4+8,4)*C(4+11,8) = C(12,4)*C(15,8) = 495*6435 = 3185325.
%t A105944 Table[Binomial[n+8,n]Binomial[n+11,8],{n,0,30}] (* _Harvey P. Dale_, Apr 26 2018 *)
%o A105944 (Magma)
%o A105944 A105944:= func< n | Binomial(n+8,8)*Binomial(n+11,8) >;
%o A105944 [A105944(n): n in [0..40]]; // _G. C. Greubel_, Mar 10 2025
%o A105944 (SageMath)
%o A105944 def A105994(n): return binomial(n+8,8)*binomial(n+11,8)
%o A105944 print([A105994(n) for n in range(41)]) # _G. C. Greubel_, Mar 10 2025
%Y A105944 Cf. A030648, A062145.
%K A105944 easy,nonn
%O A105944 0,1
%A A105944 _Zerinvary Lajos_, Apr 27 2005
%E A105944 More terms from _Colin Barker_, Jan 28 2013