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A107420 a(n) = binomial(n+5,5)*binomial(n+8,8).

%I A107420 #19 Mar 10 2025 05:07:44
%S A107420 1,54,945,9240,62370,324324,1387386,5096520,16563690,48668620,
%T A107420 131405274,330142176,779502360,1743502320,3718285560,7601828256,
%U A107420 14966099379,28482196050,52568991475,94362067800,165133618650,282337298100,472506635250,775303893000,1249100716500
%N A107420 a(n) = binomial(n+5,5)*binomial(n+8,8).
%H A107420 T. D. Noe, <a href="/A107420/b107420.txt">Table of n, a(n) for n = 0..1000</a>
%H A107420 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A107420 From _Chai Wah Wu_, Apr 10 2021: (Start)
%F A107420 a(n) = 14*a(n-1) - 91*a(n-2) + 364*a(n-3) - 1001*a(n-4) + 2002*a(n-5) - 3003*a(n-6) + 3432*a(n-7) - 3003*a(n-8) + 2002*a(n-9) - 1001*a(n-10) + 364*a(n-11) - 91*a(n-12) + 14*a(n-13) - a(n-14) for n > 13.
%F A107420 G.f.: (1 + 40*x + 280*x^2 + 560*x^3 + 350*x^4 + 56*x^5)/(1 - x)^14. (End)
%F A107420 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A107420 Sum_{n>=0} 1/a(n) = 2200*Pi^2 - 19150081/882.
%F A107420 Sum_{n>=0} (-1)^n/a(n) = 693421/490 - 20*Pi^2 - 12288*log(2)/7. (End)
%e A107420 a(0) = C(0+5,5)*C(0+8,8) = C(5,5)*C(8,8) = 1*1 = 1.
%e A107420 a(9) = C(9+5,5)*C(9+8,8) = C(14,5)*C(17,8) = 2002*24310 = 48668620.
%t A107420 a[n_] := Binomial[n + 5, 5] * Binomial[n + 8, 8]; Array[a, 30, 0] (* _Amiram Eldar_, Sep 06 2022 *)
%o A107420 (PARI) for(n=0,29,print1(binomial(n+5,5)*binomial(n+8,8),","))
%o A107420 (Magma)
%o A107420 A107420:= func< n | Binomial(n+5,n)*Binomial(n+8,n) >;
%o A107420 [A107420(n): n in [0..40]]; // _G. C. Greubel_, Mar 10 2025
%o A107420 (SageMath)
%o A107420 def A107420(n): return binomial(n+5,n)*binomial(n+8,n)
%o A107420 print([A107420(n) for n in range(41)]) # _G. C. Greubel_, Mar 10 2025
%Y A107420 Cf. A062145.
%K A107420 easy,nonn
%O A107420 0,2
%A A107420 _Zerinvary Lajos_, May 26 2005
%E A107420 More terms from _Rick L. Shepherd_, May 27 2005