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 A132755 #46 Nov 29 2024 20:40:21
%S A132755 0,13,27,42,58,75,93,112,132,153,175,198,222,247,273,300,328,357,387,
%T A132755 418,450,483,517,552,588,625,663,702,742,783,825,868,912,957,1003,
%U A132755 1050,1098,1147,1197,1248,1300,1353,1407,1462,1518,1575
%N A132755 a(n) = n*(n + 25)/2.
%H A132755 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132755 Let f(n,i,a) = Sum_{k=0..n-i} (binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j)), then a(n) = -f(n, n-1, 13), for n>=1. - _Milan Janjic_, Dec 20 2008
%F A132755 a(n) = n + a(n-1) + 12 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A132755 a(n) = 13*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F A132755 a(0)=0, a(1)=13, a(2)=27; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Aug 09 2014
%F A132755 From _Amiram Eldar_, Jan 10 2021: (Start)
%F A132755 Sum_{n>=1} 1/a(n) = 2*A001008(25)/(25*A002805(25)) = 34052522467/111546435000.
%F A132755 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/25 - 19081066231/334639305000. (End)
%F A132755 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A132755 G.f.: x*(12*x - 13)/(x-1)^3.
%F A132755 E.g.f.: exp(x)*x*(26 + x)/2.
%F A132755 a(n) = A132767(n)/2. (End)
%t A132755 Table[(n(n+25))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,27},50] (* _Harvey P. Dale_, Aug 09 2014 *)
%o A132755 (Magma) [n*(n + 25)/2 : n in [0..50]]; // _Wesley Ivan Hurt_, Jan 23 2017
%o A132755 (PARI) a(n)=n*(n+25)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A132755 Cf. A000217, A001008, A002805, A056126, A132767.
%K A132755 nonn,easy
%O A132755 0,2
%A A132755 _Omar E. Pol_, Aug 28 2007