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 A104675 #35 Mar 01 2025 11:16:57
%S A104675 6,14,24,36,50,66,84,104,126,150,176,204,234,266,300,336,374,414,456,
%T A104675 500,546,594,644,696,750,806,864,924,986,1050,1116,1184,1254,1326,
%U A104675 1400,1476,1554,1634,1716,1800,1886,1974,2064,2156,2250,2346,2444,2544,2646
%N A104675 a(n) = C(n+1,n) * C(n+6,1).
%H A104675 Colin Barker, <a href="/A104675/b104675.txt">Table of n, a(n) for n = 0..1000</a>
%H A104675 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A104675 a(n) = (n+1)*(n+6) = A028557(n+1). - _R. J. Mathar_, May 19 2008
%F A104675 a(n) = 2*n + a(n-1) + 6 (with a(0)=6). _Vincenzo Librandi_, Nov 13 2010
%F A104675 From _Colin Barker_, Apr 06 2017: (Start)
%F A104675 G.f.: 2*(3 - 2*x) / (1 - x)^3.
%F A104675 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)
%F A104675 E.g.f.: exp(x)*(x^2 + 8x + 6). - _Indranil Ghosh_, Apr 06 2017
%F A104675 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104675 Sum_{n>=0} 1/a(n) = 137/300.
%F A104675 Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/5 - 47/300. (End)
%e A104675 If n=0 then C(0+1,0+0) * C(0+6,1) = C(1,0) * C(6,1) = 1*6 = 6.
%e A104675 If n=5 then C(5+1,5+0) * C(5+6,1) = C(6,5) * C(11,1) = 6*11 = 66.
%t A104675 Table[Binomial[n + 1, n] Binomial[n + 6, 1], {n, 0, 48}] (* or *)
%t A104675 CoefficientList[Series[2 (3 - 2 x)/(1 - x)^3, {x, 0, 49}], x] (* or *)
%t A104675 LinearRecurrence[{3, -3, 1}, {6, 14, 24}, 49] (* _Michael De Vlieger_, Apr 06 2017 *)
%o A104675 (PARI) Vec(2*(3 - 2*x) / (1 - x)^3 + O(x^80)) \\ _Colin Barker_, Apr 06 2017
%o A104675 (PARI) a(n)=(n+6)*(n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A104675 (Python)
%o A104675 from sympy import binomial
%o A104675 def a(n): return binomial(n + 1, n) * binomial(n + 6, 1) # _Indranil Ghosh_, Apr 06 2017
%o A104675 (Magma) [(n+1)*(n+6): n in [0..50]]; // _G. C. Greubel_, Mar 01 2025
%Y A104675 Cf. A002522, A028557, A062190.
%K A104675 easy,nonn
%O A104675 0,1
%A A104675 _Zerinvary Lajos_, Apr 22 2005