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 A180415 #25 Nov 14 2023 21:26:21
%S A180415 1,3,6,11,19,31,48,71,101,139,186,243,311,391,484,591,713,851,1006,
%T A180415 1179,1371,1583,1816,2071,2349,2651,2978,3331,3711,4119,4556,5023,
%U A180415 5521,6051,6614,7211,7843,8511,9216,9959,10741,11563,12426,13331,14279,15271,16308
%N A180415 a(n) = (n^3 - 3n^2 + 14n - 6)/6.
%C A180415 Binomial transform of 0,1,1,0,bar(1,-1), where bar(..) denotes a periodically repeated sequence.
%C A180415 If the offset is set to 0, this is the binomial transform of the quasi-finite sequence 1,2,1,1,bar(0).
%H A180415 Paolo P. Lava, <a href="/A180415/b180415.txt">Table of n, a(n) for n = 1..1000</a>
%H A180415 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A180415 G.f. x*(x^3 - x + 1)/(x-1)^4.
%e A180415 Representation as binomial transform: a(4) = 11 = (1, 2, 1, 1) dot (1, 3, 3, 1) = (1 + 6 + 3 + 1).
%t A180415 Table[(n^3-3n^2+14n-6)/6,{n,60}] (* _Harvey P. Dale_, Mar 04 2011 *)
%K A180415 nonn,easy
%O A180415 1,2
%A A180415 _Gary W. Adamson_, Sep 02 2010
%E A180415 Sequence extended, nomenclature of variables normalized, g.f. multiplied by x, binomial transforms clarified - _R. J. Mathar_, Sep 04 2010