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 A002999 #38 Jul 17 2025 12:29:58
%S A002999 1,2,6,18,56,170,492,1358,3600,9234,23060,56342,135192,319514,745500,
%T A002999 1720350,3932192,8912930,20054052,44826662,99614760,220201002,
%U A002999 484442156,1061158958,2315255856,5033164850,10905190452,23555211318,50734301240,108984795194,233538846780
%N A002999 Expansion of (1 + x*exp(x))^2.
%C A002999 a(n) is the number of binary words of length n where exactly one of each kind of letter that appears is marked. - _John Tyler Rascoe_, Jul 16 2025
%H A002999 T. D. Noe, <a href="/A002999/b002999.txt">Table of n, a(n) for n = 0..500</a>
%H A002999 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25,38,-28,8)
%F A002999 From _Ralf Stephan_, Sep 02 2003: (Start)
%F A002999 a(0) = 1, a(n) = (n^2 - n)*2^n/4 + 2*n.
%F A002999 a(n) = A003013(n) + n = A001815(n) + 2*n. (End)
%F A002999 G.f.: 1+(2*x*(7*x^3-10*x^2+5*x-1))/((x-1)^2*(2*x-1)^3). - _Harvey P. Dale_, Apr 04 2011
%e A002999 a(2) = 6 counts: (1#,1), (1,1#), (1#,2#), (2#,1#), (2#,2), (2,2#) where # denotes a mark. - _John Tyler Rascoe_, Jul 16 2025
%t A002999 CoefficientList[Series[1+(2x(7x^3-10x^2+5x-1))/((x-1)^2 (2x-1)^3), {x,0,30}],x] (* _Harvey P. Dale_, Apr 04 2011 *)
%t A002999 Table[If[n == 0, 1, (n^2 - n) 2^n/4 + 2*n], {n, 0, 30}] (* _T. D. Noe_, Apr 04 2011 *)
%o A002999 (PARI)
%o A002999 A_x(N) = {my(x='x+O('x^(N+1))); Vec(serlaplace((1+x*exp(x))^2))} \\ _John Tyler Rascoe_, Jul 16 2025
%Y A002999 Cf. A048482, A001787, A005183.
%Y A002999 Cf. A003013, A001815.
%K A002999 nonn,easy
%O A002999 0,2
%A A002999 _N. J. A. Sloane_