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 A181440 #21 Oct 18 2024 13:45:08
%S A181440 2,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A181440 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A181440 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72
%N A181440 a(1) = 2; for n > 1, a(n) = A000217(n)-(sum of previous terms).
%C A181440 2 followed by A065475, or A000027 with first and second term interchanged.
%C A181440 It can be observed that this sequence is an "autosequence", that is a sequence which is identical to its inverse binomial transform, except for signs. More precisely, it is an autosequence "of the second kind", since the main diagonal of the successive differences array is twice the first upper diagonal. - _Jean-François Alcover_, Jul 25 2016
%H A181440 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%H A181440 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F A181440 G.f.: x*(2-x)*(1-x+x^2) / (1-x)^2. - _Joerg Arndt_, Jul 25 2016
%t A181440 a = {2}; Do[AppendTo[a, ((n^2 + n)/2) - Total@ a], {n, 2, 72}]; a (* _Michael De Vlieger_, Jul 25 2016 *)
%o A181440 (Magma) S:=[2]; s:=2; for n in [2..80] do a:=Binomial(n+1, 2)-s; Append(~S, a); s+:=a; end for; S;
%Y A181440 Cf. A000027 (natural numbers), A000217 (triangular numbers), A065475 (natural numbers excluding 2).
%K A181440 easy,nonn
%O A181440 1,1
%A A181440 _Giovanni Teofilatto_, Oct 20 2010
%E A181440 Edited by _Klaus Brockhaus_, Oct 26 2010
%E A181440 A171950 and A181440 are two different edited versions of a sequence submitted by Giovanni Teofilatto. - _N. J. A. Sloane_, Oct 29 2010