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 A132758 #33 Nov 29 2024 20:39:55
%S A132758 0,16,33,51,70,90,111,133,156,180,205,231,258,286,315,345,376,408,441,
%T A132758 475,510,546,583,621,660,700,741,783,826,870,915,961,1008,1056,1105,
%U A132758 1155,1206,1258,1311,1365,1420,1476,1533,1591,1650
%N A132758 a(n) = n*(n + 31)/2.
%H A132758 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132758 a(n) = n*(n + 31)/2.
%F A132758 If we define f(n,i,r) = Sum_{k=0..n-i} binomial(n,k) * Stirling1(n-k,i) * Product_{j=0..k-1} (-r-j), then a(n) = -f(n,n-1,16) for n>=1. - _Milan Janjic_, Dec 20 2008
%F A132758 a(n) = n + a(n-1) + 15 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A132758 a(0)=0, a(1)=16, a(2)=33; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jun 21 2012
%F A132758 a(n) = 16*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F A132758 From _Amiram Eldar_, Jan 11 2021: (Start)
%F A132758 Sum_{n>=1} 1/a(n) = 2*A001008(31)/(31*A002805(31)) = 290774257297357/1119127534925400.
%F A132758 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/31 - 7313175618421/159875362132200. (End)
%F A132758 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A132758 G.f.: x*(15*x - 16)/(x-1)^3.
%F A132758 E.g.f.: exp(x)*x*(32 + x)/2.
%F A132758 a(n) = A132773(n)/2. (End)
%t A132758 Table[(n(n+31))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,16,33},50] (* _Harvey P. Dale_, Jun 21 2012 *)
%o A132758 (PARI) a(n)=n*(n+31)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A132758 Cf. A000217, A001008, A002805, A056126, A132773.
%K A132758 nonn,easy
%O A132758 0,2
%A A132758 _Omar E. Pol_, Aug 28 2007