This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104473 #48 Mar 05 2025 05:29:12
%S A104473 15,63,168,360,675,1155,1848,2808,4095,5775,7920,10608,13923,17955,
%T A104473 22800,28560,35343,43263,52440,63000,75075,88803,104328,121800,141375,
%U A104473 163215,187488,214368,244035,276675,312480,351648,394383,440895,491400,546120,605283,669123
%N A104473 a(n) = binomial(n+2,2)*binomial(n+6,2).
%H A104473 Vincenzo Librandi, <a href="/A104473/b104473.txt">Table of n, a(n) for n = 0..1000</a>
%H A104473 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A104473 a(n) = (1/4)*(n+1)*(n+2)*(n+5)*(n+6).
%F A104473 a(n) = A034856(n+2)^2 - 1. - _J. M. Bergot_, Dec 14 2010
%F A104473 G.f.: 3*(5-4*x+x^2)/(1-x)^5. - _Colin Barker_, Sep 21 2012
%F A104473 a(n) = Sum_{i=1..n+1} i*(i+2)*(i+4). - _Bruno Berselli_, Apr 28 2014
%F A104473 a(n) = A000217(n)*A000217(n+4) = 3*A033275(n+4). - _R. J. Mathar_, Nov 29 2015
%F A104473 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104473 Sum_{n>=0} 1/a(n) = 43/450.
%F A104473 Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/15 - 154/225. (End)
%F A104473 From _G. C. Greubel_, Mar 05 2025: (Start)
%F A104473 a(n) = 90*A000579(n+6)/A000279(n+3).
%F A104473 E.g.f.: (1/4)*(60 + 192*x + 114*x^2 + 20*x^3 + x^4)*exp(x). (End)
%e A104473 a(0) = C(0+2,2)*C(0+6,2) = C(2,2)*C(6,2) = 1*15 = 155.
%e A104473 a(6) = 1*3*5 + 2*4*6 + 3*5*7 + 4*6*8 + 5*7*9 + 6*8*10 + 7*9*11 = 1848.
%t A104473 f[n_] := Binomial[n + 2, 2] Binomial[n + 6, 2]; Table[f[n], {n,0,40}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%t A104473 CoefficientList[Series[3 (5-4*x+x^2)/(1-x)^5, {x,0,40}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%o A104473 (PARI) a(n)=binomial(n+2,2)*binomial(n+6,2) \\ _Charles R Greathouse IV_, Jun 07 2013
%o A104473 (Magma) [Binomial(n+2, 2)*Binomial(n+6, 2): n in [0..50]]; // _Vincenzo Librandi_, Apr 28 2014
%o A104473 (SageMath)
%o A104473 def A104473(n): return binomial(n+2,2)*binomial(n+6,2)
%o A104473 print([A104473(n) for n in range(51)]) # _G. C. Greubel_, Mar 05 2025
%Y A104473 Cf. A000217, A000579, A033275, A034856, A062264.
%Y A104473 Subsequence of A085780.
%K A104473 nonn,easy
%O A104473 0,1
%A A104473 _Zerinvary Lajos_, Apr 18 2005