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 A067239 #29 May 05 2025 01:37:36
%S A067239 1,8,48,120,224,360,528,728,960,1224,1520,1848,2208,2600,3024,3480,
%T A067239 3968,4488,5040,5624,6240,6888,7568,8280,9024,9800,10608,11448,12320,
%U A067239 13224,14160,15128,16128,17160,18224,19320,20448,21608,22800,24024
%N A067239 a(0)=1, a(n) = 8*n*(2*n-1).
%C A067239 Engel expansion of cosh(1/2).
%C A067239 Also, 8 times hexagonal numbers (8*A000384(n) = A152750(n)), for n > 0. - _Omar E. Pol_, Dec 14 2008
%H A067239 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A067239 a(n) = a(n-1) + 32*n - 24 (with a(1)=8). - _Vincenzo Librandi_, Dec 15 2010
%F A067239 From _Colin Barker_, Apr 13 2012: (Start)
%F A067239 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3.
%F A067239 G.f.: (1 + 5*x + 27*x^2 - x^3)/(1-x)^3. (End)
%F A067239 E.g.f.: 1 + 8*exp(x)*x*(1 + 2*x). - _Elmo R. Oliveira_, Dec 15 2024
%F A067239 From _Amiram Eldar_, May 05 2025: (Start)
%F A067239 Sum_{n>=0} 1/a(n) = log(2)/4 + 1.
%F A067239 Sum_{n>=0} (-1)^n/a(n) = 1 - Pi/16 + log(2)/8. (End)
%t A067239 s=0;lst={s};Do[s+=n++ +8;AppendTo[lst, s], {n, 0, 8!, 32}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 16 2008 *)
%o A067239 (PARI) Vec((1+5*x+27*x^2-x^3)/(1-x)^3+O(x^99)) \\ _Charles R Greathouse IV_, Apr 13 2012
%Y A067239 Cf. A006784 for Engel expansion definition.
%Y A067239 Cf. A000384, A152750.
%K A067239 easy,nonn
%O A067239 0,2
%A A067239 _Benoit Cloitre_, Mar 03 2002