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A107422 a(n) = binomial(n+7,7) * binomial(n+10,10).

%I A107422 #16 Mar 10 2025 05:07:35
%S A107422 1,88,2376,34320,330330,2378376,13741728,66745536,281582730,
%T A107422 1056804320,3593134688,11224833984,32583198648,88687996320,
%U A107422 228054847680,557467405440,1302209017395,2919831983640,6308278977000,13175740578000,26680874670450,52514737446600
%N A107422 a(n) = binomial(n+7,7) * binomial(n+10,10).
%H A107422 Andrew Howroyd, <a href="/A107422/b107422.txt">Table of n, a(n) for n = 0..1000</a>
%H A107422 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
%F A107422 From _Chai Wah Wu_, Apr 10 2021: (Start)
%F A107422 a(n) = 18*a(n-1) - 153*a(n-2) + 816*a(n-3) - 3060*a(n-4) + 8568*a(n-5) - 18564*a(n-6) + 31824*a(n-7) - 43758*a(n-8) + 48620*a(n-9) - 43758*a(n-10) + 31824*a(n-11) - 18564*a(n-12) + 8568*a(n-13) - 3060*a(n-14) + 816*a(n-15) - 153*a(n-16) + 18*a(n-17) - a(n-18) for n > 17.
%F A107422 G.f.: (1 + 70*x + 945*x^2 + 4200*x^3 + 7350*x^4 + 5292*x^5 + 1470*x^6 + 120*x^7)/(1 - x)^18. (End)
%F A107422 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A107422 Sum_{n>=0} 1/a(n) = 175175*Pi^2/3 - 1493773847/2592.
%F A107422 Sum_{n>=0} (-1)^n/a(n) = 875*Pi^2/6 + 90112*log(2)/9 - 760090799/90720. (End)
%e A107422 If n=0 then C(0+7,7)*C(0+10,10) = C(7,7)*C(10,10) = 1*1 = 1.
%e A107422 If n=4 then C(4+7,7)*C(4+10,10) = C(11,7)*C(14,10) = 330*1001 = 330330.
%t A107422 a[n_] := Binomial[n + 7, 7] * Binomial[n + 10, 10]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)
%o A107422 (PARI) a(n)={binomial(n+7,7) * binomial(n+10,10)} \\ _Andrew Howroyd_, Nov 08 2019
%o A107422 (Magma)
%o A107422 A107422:= func< n | Binomial(n+7,n)*Binomial(n+10,n) >;
%o A107422 [A107422(n): n in [0..40]]; // _G. C. Greubel_, Mar 09 2025
%o A107422 (SageMath)
%o A107422 def A107422(n): return binomial(n+7,n)*binomial(n+10,n)
%o A107422 print([A107422(n) for n in range(41)]) # _G. C. Greubel_, Mar 09 2025
%Y A107422 Cf. A062145.
%K A107422 easy,nonn
%O A107422 0,2
%A A107422 _Zerinvary Lajos_, May 26 2005
%E A107422 Terms a(8) and beyond from _Andrew Howroyd_, Nov 08 2019