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 A104679 #25 Aug 30 2022 09:44:25 %S A104679 252,2772,16632,72072,252252,756756,2018016,4900896,11027016,23279256, %T A104679 46558512,88884432,162954792,288304632,494236512,823727520,1338557220, %U A104679 2125943820,3307023720,5047562520,7571343780,11176745580,16257084480,23325382080,33044291280 %N A104679 a(n) = C(n+5,5)*C(n+10,5). %H A104679 Colin Barker, <a href="/A104679/b104679.txt">Table of n, a(n) for n = 0..1000</a> %H A104679 <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 A104679 G.f.: 252 / (1-x)^11. - _Colin Barker_, Feb 07 2015 %F A104679 a(n) = A000389(n+5)*A000389(n+10) = 252*A001287(n+11). - _R. J. Mathar_, Nov 29 2015 %F A104679 From _Amiram Eldar_, Aug 30 2022: (Start) %F A104679 Sum_{n>=0} 1/a(n) = 5/1134. %F A104679 Sum_{n>=0} (-1)^n/a(n) = 1280*log(2)/63 - 447047/31752. (End) %e A104679 If n=0 then C(0+5,0+0)*C(0+10,5) = C(5,0)*C(10,5) = 1*252 = 252. %e A104679 If n=4 then C(4+5,4+0)*C(4+10,5) = C(9,4)*C(14,5) = 126*2002 = 252252. %t A104679 Table[Binomial[n+5,n]Binomial[n+10,5],{n,0,20}] (* _Harvey P. Dale_, Feb 06 2015 *) %o A104679 (PARI) Vec(252/(1-x)^11 + O(x^100)) \\ _Colin Barker_, Feb 07 2015 %o A104679 (Magma) [Binomial(n+5,n)*Binomial(n+10,5): n in [0..30]]; // _G. C. Greubel_, Nov 25 2017 %Y A104679 Cf. A062190. %K A104679 easy,nonn %O A104679 0,1 %A A104679 _Zerinvary Lajos_, Apr 22 2005 %E A104679 Corrected and extended by _Harvey P. Dale_, Feb 06 2015