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 A069477 #25 Feb 08 2025 19:35:33
%S A069477 390,750,1230,1830,2550,3390,4350,5430,6630,7950,9390,10950,12630,
%T A069477 14430,16350,18390,20550,22830,25230,27750,30390,33150,36030,39030,
%U A069477 42150,45390,48750,52230,55830,59550,63390,67350,71430,75630,79950,84390,88950,93630,98430,103350
%N A069477 a(n) = 60*n^2 + 180*n + 150.
%C A069477 First differences of A068236, successive differences of (n+1)^5 - n^5 (A022521).
%H A069477 Vincenzo Librandi, <a href="/A069477/b069477.txt">Table of n, a(n) for n = 1..10000</a>
%H A069477 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A069477 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=390, a(2)=750, a(3)=1230. - _Harvey P. Dale_, Apr 06 2012
%F A069477 Sum_{n>=1} 1/a(n) = (Pi/60)*tanh(Pi/2) - 1/25. - _Amiram Eldar_, Jan 27 2022
%F A069477 From _Elmo R. Oliveira_, Feb 08 2025: (Start)
%F A069477 G.f.: 30*x*(5*x^2 - 14*x + 13)/(1-x)^3.
%F A069477 E.g.f.: 30*(exp(x)*(2*x^2 + 8*x + 5) - 5).
%F A069477 a(n) = 30*A001844(n+1) = 15*A069894(n+1). (End)
%t A069477 Table[30 (2 n^2 + 6 n + 5), {n, 1, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 19 2011 *)
%t A069477 LinearRecurrence[{3,-3,1},{390,750,1230},40] (* _Harvey P. Dale_, Apr 06 2012 *)
%o A069477 (Magma) [30*(2*n^2 + 6*n + 5): n in [1..40]]; // _Vincenzo Librandi_, Nov 23 2011
%o A069477 (PARI) a(n)=60*n^2+180*n+150 \\ _Charles R Greathouse IV_, Nov 23 2011
%Y A069477 Cf. A001844, A022521, A068236, A069477, A069894, A101096.
%K A069477 nonn,easy
%O A069477 1,1
%A A069477 Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Apr 11 2002