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 A369491 #14 Feb 27 2024 10:57:54
%S A369491 1,2,4,10,22,46,94,190,382,766,1534,3070,6142,12286,24574,49150,98302,
%T A369491 196606,393214,786430,1572862,3145726,6291454,12582910,25165822,
%U A369491 50331646,100663294,201326590,402653182,805306366,1610612734,3221225470,6442450942,12884901886,25769803774
%N A369491 a(n) = n! * [x^n] (2*x - 4*exp(x) + 3*exp(2*x) + 3) / 2.
%H A369491 Paolo Xausa, <a href="/A369491/b369491.txt">Table of n, a(n) for n = 0..2000</a>
%H A369491 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A369491 a(n) = [x^n] ((x + 1)*(2*x^2 - 2*x + 1))/((2*x - 1)*(x - 1)).
%F A369491 a(n) = 3*a(n - 1) - 2*a(n - 2) for n >= 4.
%p A369491 gf := ((x + 1)*(2*x^2 - 2*x + 1))/((2*x - 1)*(x - 1)):
%p A369491 ser := series(gf, x, 40): seq(coeff(ser, x, n), n = 0..34);
%p A369491 a := proc(n) option remember; ifelse(n < 4, [1, 2, 4, 10][n+1],
%p A369491 3*a(n - 1) - 2*a(n - 2)) end: seq(a(n), n = 0..34);
%t A369491 LinearRecurrence[{3, -2}, {1, 2, 4, 10}, 50] (* _Paolo Xausa_, Feb 27 2024 *)
%Y A369491 Cf. A033484 (similar, 'missing' 2).
%K A369491 nonn,easy
%O A369491 0,2
%A A369491 _Peter Luschny_, Jan 24 2024