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 A295519 #10 Dec 18 2017 04:14:59
%S A295519 0,1,5,22,100,493,2701,16678,116704,923473,8204077,81069166,882762292,
%T A295519 10503611245,135576241957,1886597854894,28151936397856,
%U A295519 448397396131969,7592570340752053,136187683731334054,2579494839314653540,51445637954467827661
%N A295519 a(n) = e^3 * Sum_{k=0..n-1} Gamma(k + 1, 3).
%F A295519 a(n) = (3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) for n >= 3.
%F A295519 E.g.f.: exp(x+2)*(Ei(1,2-2*x)-Ei(1,2)). - _Robert Israel_, Dec 17 2017
%p A295519 a := proc(n) option remember; if n=0 then 0 elif n=1 then 1 elif n=2 then 5 else
%p A295519 (3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) fi end: seq(a(n), n=0..21);
%t A295519 a[n_] := E^3 Sum[Gamma[k + 1, 3], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]
%o A295519 (PARI) a=vector(1000); a[1]=1;a[2]=5;a[3]=22;for(n=4, #a, a[n] = (n+3)*a[n-1]+(4-4*n)*a[n-2]+(3*n-6)*a[n-3]); va=concat(0, vector(1000, n, a[n])) \\ _Altug Alkan_, Dec 17 2017
%Y A295519 Cf A053486, A295518.
%K A295519 nonn
%O A295519 0,3
%A A295519 _Peter Luschny_, Dec 17 2017