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A105946 a(n) = C(n+3,3) * C(n+5,5).

%I A105946 #25 Feb 22 2025 04:02:40
%S A105946 1,24,210,1120,4410,14112,38808,95040,212355,440440,858858,1589952,
%T A105946 2815540,4798080,7907040,12651264,19718181,30020760,44753170,65456160,
%U A105946 94093230,133138720,185679000,255528000,347358375,466849656,620854794,817586560,1066825320
%N A105946 a(n) = C(n+3,3) * C(n+5,5).
%H A105946 G. C. Greubel, <a href="/A105946/b105946.txt">Table of n, a(n) for n = 0..1000</a>
%H A105946 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A105946 G.f.: (1 + 15*x + 30*x^2 + 10*x^3)/(1-x)^9. - _Colin Barker_, Jan 28 2013
%F A105946 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A105946 Sum_{n>=0} 1/a(n) = 75*Pi^2/2 - 5905/16.
%F A105946 Sum_{n>=0} (-1)^n/a(n) = 160*log(2) - 5*Pi^2/4 - 4685/48. (End)
%F A105946 E.g.f.: (1/6!)*(720 + 16560*x + 58680*x^2 + 67320*x^3 + 32850*x^4 + 7686*x^5 + 893*x^6 + 49*x^7 + x^8)*exp(x). - _G. C. Greubel_, Feb 22 2025
%e A105946 If n=0 then C(0+5,0)*C(0+3,3) = C(5,0)*C(3,3) = 1*1 = 1.
%e A105946 If n=15 then C(15+5,15)*C(15+3,3) = C(20,15)*C(18,3) = 15504*816 = 12651264.
%p A105946 A105946:=n->binomial(n+5,n)*binomial(n+3,3); seq(A105946(n), n=0..100); # _Wesley Ivan Hurt_, Nov 26 2013
%t A105946 Table[Binomial[n+5,n]*Binomial[n+3,3], {n,0,100}] (* _Wesley Ivan Hurt_, Nov 26 2013 *)
%o A105946 (Magma)
%o A105946 A105946:= func< n | Binomial(n+3,3)*Binomial(n+5,5) >;
%o A105946 [A105946(n): n in [0..40]]; // _G. C. Greubel_, Feb 22 2025
%o A105946 (SageMath)
%o A105946 def A105946(n): return binomial(n+3,3)*binomial(n+5,5)
%o A105946 print([A105946(n) for n in range(41)]) # _G. C. Greubel_, Feb 22 2025
%Y A105946 Cf. A062196.
%K A105946 easy,nonn
%O A105946 0,2
%A A105946 _Zerinvary Lajos_, Apr 27 2005
%E A105946 More terms from _Colin Barker_, Jan 28 2013