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A105250 a(n) = binomial(n+3,n)*binomial(n+7,n).

%I A105250 #28 Mar 04 2025 08:12:35
%S A105250 1,32,360,2400,11550,44352,144144,411840,1061775,2516800,5562128,
%T A105250 11583936,22926540,43411200,79070400,139163904,237557133,394558560,
%U A105250 639331000,1013012000,1572701130,2396496960,3589794000,5293080000,7691506875,11026544256,15610063392
%N A105250 a(n) = binomial(n+3,n)*binomial(n+7,n).
%H A105250 T. D. Noe, <a href="/A105250/b105250.txt">Table of n, a(n) for n = 0..1000</a>
%H A105250 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A105250 G.f.: (1+21*x+63*x^2+35*x^3)/(1-x)^11. - _Colin Barker_, Jan 21 2013
%F A105250 a(n) = 11*a(n-1) -55*a(n-2) +165*a(n-3) -330*a(n-4) +462*a(n-5) -462*a(n-6) +330*a(n-7) -165*a(n-8) +55*a(n-9) -11*a(n-10) +a(n-11). - _Wesley Ivan Hurt_, May 24 2021
%F A105250 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A105250 Sum_{n>=0} 1/a(n) = 98*Pi^2 - 72464/75.
%F A105250 Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2 + 1792*log(2)/5 - 15827/50. (End)
%e A105250 a(0): C(0+3,0)*C(0+7,0) = C(3,0)*C(7,0) = 1*1 = 1;
%e A105250 a(10): C(10+3,10)*C(10+7,10) = C(13,10)*(17,10) = 286*19448 = 5562128.
%t A105250 f[n_] := Binomial[n + 3, n]Binomial[n + 7, n]; Table[ f[n], {n, 0, 23}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%o A105250 (Magma) [Binomial(n+3,n)*Binomial(n+7,n): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%o A105250 (SageMath)
%o A105250 def A105250(n): return binomial(n+3,n)*binomial(n+7,n)
%o A105250 print([A105250(n) for n in range(31)]) # _G. C. Greubel_, Mar 04 2025
%Y A105250 Cf. A062264.
%K A105250 easy,nonn
%O A105250 0,2
%A A105250 _Zerinvary Lajos_, Apr 14 2005
%E A105250 More terms from _Robert G. Wilson v_, Apr 20 2005