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A105254 a(n) = binomial(n+7,n)*binomial(n+11,n).

%I A105254 #23 Mar 04 2025 07:36:23
%S A105254 1,96,2808,43680,450450,3459456,21237216,109219968,486370170,
%T A105254 1921462400,6859620768,22449667968,68128506264,193501082880,
%U A105254 518306472000,1317650231040,3196331224515,7432299594720,16630917303000,35933837940000,75191555889450,152770145299200
%N A105254 a(n) = binomial(n+7,n)*binomial(n+11,n).
%H A105254 G. C. Greubel, <a href="/A105254/b105254.txt">Table of n, a(n) for n = 0..1000</a>
%H A105254 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).
%F A105254 G.f.: (1 + 77*x + 1155*x^2 + 5775*x^3 + 11550*x^4 + 9702*x^5 + 3234*x^6 + 330*x^7)/(1-x)^19. - _Colin Barker_, Jan 21 2013
%F A105254 From _Amiram Eldar_, Sep 04 2022: (Start)
%F A105254 Sum_{n>=0} 1/a(n) = 308308*Pi^2/3 - 16431524791/16200.
%F A105254 Sum_{n>=0} (-1)^n/a(n) = 1232*Pi^2/3 + 360448*log(2)/45 - 108911693/11340. (End)
%e A105254 a(0): C(0+7,0)*C(0+11,0) = C(7,0)*C(11,0) = 1*1 = 1;
%e A105254 a(8): C(8+7,8)*C(8+11,8) = C(15,8)*(19,8) = 6435*75582 = 486370170.
%t A105254 f[n_] := Binomial[n + 7, n]Binomial[n + 11, n]; Table[ f[n], {n, 0, 19}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%o A105254 (Magma) [Binomial(n+7,n)*Binomial(n+11,n): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%o A105254 (SageMath)
%o A105254 def A105254(n): return binomial(n+7,n)*binomial(n+11,n)
%o A105254 print([A105254(n) for n in range(31)]) # _G. C. Greubel_, Mar 04 2025
%Y A105254 Cf. A062264.
%K A105254 easy,nonn
%O A105254 0,2
%A A105254 _Zerinvary Lajos_, Apr 14 2005
%E A105254 More terms from _Robert G. Wilson v_, Apr 20 2005
%E A105254 More terms from _Colin Barker_, Jan 21 2013