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A105943 a(n) = binomial(n+7,7) * binomial(n+10,7).

%I A105943 #26 Mar 11 2025 04:37:59
%S A105943 120,2640,28512,205920,1132560,5096520,19631040,66745536,204787440,
%T A105943 576438720,1507608960,3700494720,8593371072,19004570640,40244973120,
%U A105943 81980500800,161264274600,307350735120,569168028000,1026681084000,1807851474000,3113521983000
%N A105943 a(n) = binomial(n+7,7) * binomial(n+10,7).
%H A105943 T. D. Noe, <a href="/A105943/b105943.txt">Table of n, a(n) for n = 0..1000</a>
%H A105943 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F A105943 G.f.: 24*(5 + 35*x + 63*x^2 +35*x^3 + 5*x^4)/(1-x)^15. - _Harvey P. Dale_, Nov 14 2011
%F A105943 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A105943 Sum_{n>=0} 1/a(n) = 114905939/6480 - 5390*Pi^2/3.
%F A105943 Sum_{n>=0} (-1)^n/a(n) = 14336*log(2)/9 - 3577279/3240. (End)
%e A105943 If n=0 then C(0+7,0)*C(0+10,7) = C(7,0)*C(10,7) = 1*120 = 120.
%e A105943 If n=6 then C(6+7,6)*C(6+10,7) = C(13,6)*C(16,7) = 1716*11440 = 19631040.
%p A105943 A105943:=n->binomial(n+7,n)*binomial(n+10,7): seq(A105943(n), n=0..40); # _Wesley Ivan Hurt_, Apr 18 2017
%t A105943 Table[Binomial[n+7,n]Binomial[n+10,7],{n,0,30}] (* _Harvey P. Dale_, Nov 14 2011 *)
%o A105943 (Python)
%o A105943 A105943_list, m = [], [3432, -3432, 1320, 0]+[120]*11
%o A105943 for _ in range(10**2):
%o A105943     A105943_list.append(m[-1])
%o A105943     for i in range(14):
%o A105943         m[i+1] += m[i] # _Chai Wah Wu_, Jan 24 2016
%o A105943 (Magma)
%o A105943 A105943:= func< n | Binomial(n+7,7)*Binomial(n+10,7) >;
%o A105943 [A105943(n): n in [0..40]]; // _G. C. Greubel_, Mar 10 2025
%o A105943 (SageMath)
%o A105943 def A105943(n): return binomial(n+7,7)*binomial(n+10,7)
%o A105943 print([A105943(n) for n in range(41)]) # _G. C. Greubel_, Mar 10 2025
%Y A105943 Cf. A062145.
%K A105943 easy,nonn
%O A105943 0,1
%A A105943 _Zerinvary Lajos_, Apr 27 2005
%E A105943 More terms from _Harvey P. Dale_, Nov 14 2011