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 A302908 #10 Aug 20 2021 05:57:31
%S A302908 1,-4,22,-164,1589,-19136,276224,-4650752,89486849,-1937066524,
%T A302908 46589361346,-1232598278044,35574999098357,-1112321525118584,
%U A302908 37454195074337084,-1351244122522567256,51999107708388285089,-2126115743789144316212,92045274930441985100494
%N A302908 Expansion of e.g.f. 6*exp(-x)/(6 + x*(3 + x)*(6 + x)).
%F A302908 E.g.f.: 1 / Sum_{k>=0} ((k + 1)*(k + 2)*(k + 3)/6)*x^k/k! = 1 / Sum_{k>=0} A000292(k+1)*x^k/k!.
%F A302908 D-finite with recurrence +6*a(n) +6*(3*n+1)*a(n-1) +9*(n+2)*(n-1)*a(n-2) +(n-1)*(n-2)*(n+9)*a(n-3) +(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 20 2021
%e A302908 6*exp(-x)/(6 + x*(3 + x)*(6 + x)) = 1 - 4*x/1! + 22*x^2/2! - 164*x^3/3! + 1589*x^4/4! - 19136*x^5/5! + 276224*x^6/6! - 4650752*x^7/7! + ...
%p A302908 a:=series(6*exp(-x)/(6 + x*(3 + x)*(6 + x)),x=0,19): seq(n!*coeff(a,x,n),n=0..18); # _Paolo P. Lava_, Mar 26 2019
%t A302908 nmax = 18; CoefficientList[Series[6 Exp[-x]/(6 + x (3 + x) (6 + x)), {x, 0, nmax}], x] Range[0, nmax]!
%o A302908 (PARI) x='x+O('x^99); Vec(serlaplace(6*exp(-x)/(6+x*(3+x)*(6+x)))) \\ _Altug Alkan_, Apr 15 2018
%Y A302908 Cf. A000292, A302195.
%K A302908 sign
%O A302908 0,2
%A A302908 _Ilya Gutkovskiy_, Apr 15 2018