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 A294040 #7 Nov 15 2017 03:29:17
%S A294040 0,1,14,321,13684,986345,108504786,16926795529,3554627458376,
%T A294040 966858672295089,330665665961417590,138879579704199815921,
%U A294040 70273067330329989586044,42163840398198057552632281,29599015959535037299068127994,24034400959142450300350904324985
%N A294040 a(n) = e*(Gamma(2*n,1) - Gamma(n,1)).
%H A294040 Robert Israel, <a href="/A294040/b294040.txt">Table of n, a(n) for n = 0..225</a>
%F A294040 a(n) = Sum_{k=0..2n-1} (2n-1)!/k! - Sum_{k=0..n-1} (n-1)!/k! = A000522(2*n-1) - A000522(n-1). - _Robert Israel_, Nov 14 2017
%p A294040 a := n -> exp(1)*(GAMMA(2*n,1) - GAMMA(n,1)):
%p A294040 seq(simplify(a(n)), n=0..15);
%p A294040 # Alternative:
%p A294040 A000522:= gfun:-rectoproc({(-x-2)*d(1+x)+(x+4)*d(x+2)-d(x+3), d(0) = 1, d(1) = 2, d(2) = 5},d(x),remember):
%p A294040 0, seq(A000522(2*n-1)-A000522(n-1),n=1..30); # _Robert Israel_, Nov 14 2017
%Y A294040 Cf. A000522, A294039.
%K A294040 nonn
%O A294040 0,3
%A A294040 _Peter Luschny_, Nov 14 2017