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 A140139 #15 Apr 21 2025 08:35:54
%S A140139 1,2,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,
%T A140139 49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,
%U A140139 95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141
%N A140139 Binomial transform of [1, 1, 2, -3, 4, -5, 6, -7, ...].
%C A140139 Apart from initial term, identical to A130773 if offsets are ignored. - _R. J. Mathar_, May 11 2008
%H A140139 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A140139 Equals A007318 * [1, 1, 2, -3, 4, -5, 6, -7, ...].
%F A140139 Sums of antidiagonal terms of the following array: 1, 1, 1, 1, 1, ... 1, 3, 5, 7, 9, ... 1, 1, 1, 1, 1, ...
%F A140139 O.g.f.: x*(1 + 2*x^2 - x^3)/(1 - x)^2. - _R. J. Mathar_, May 11 2008
%F A140139 E.g.f.: 1 - x^2/2 - exp(x)*(1 - 2*x). - _Stefano Spezia_, Apr 20 2025
%e A140139 a(4) = 7 = (1, 3, 3, 1) dot (1, 1, 2, -3) = (1 + 3 + 6 - 3).
%t A140139 LinearRecurrence[{2,-1},{1,2,5,7},71] (* _Stefano Spezia_, Apr 20 2025 *)
%Y A140139 Cf. A007318, A130773.
%K A140139 nonn,easy
%O A140139 1,2
%A A140139 _Gary W. Adamson_, May 09 2008