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 A355407 #8 Mar 09 2023 11:33:36
%S A355407 0,1,11,110,1154,13144,164136,2251920,33923760,560180160,10117886400,
%T A355407 199399132800,4275988617600,99473802624000,2502049379558400,
%U A355407 67804022648678400,1972357507107993600,61358018782620672000,2033893411878730752000,71587670846333773824000,2666700362750370895872000
%N A355407 Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^4.
%C A355407 Conjecture: For p prime, a(p) == -1 (mod p).
%F A355407 a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062137(n, k+1).
%F A355407 a(0) = 0, a(n) = n!*Sum_{k=1..n} A000292(n-k+1)*(2^k-1)/k.
%F A355407 a(n) = A000332(n+3)*n!*hypergeom([1 - n, 1, 1], [2, 5], -1). - _Peter Luschny_, Jul 01 2022
%p A355407 egf := log((1 - x)/(1 - 2*x))/(1 - x)^4: ser := series(egf, x, 22):
%p A355407 seq(n!*coeff(ser, x, n), n = 0..20); # _Peter Luschny_, Jul 01 2022
%t A355407 With[{nn=20},CoefficientList[Series[Log[((1-x)/(1-2x))]/(1-x)^4,{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Mar 09 2023 *)
%Y A355407 Cf. A000292, A000332, A062137, A355171, A355372.
%K A355407 nonn
%O A355407 0,3
%A A355407 _Mélika Tebni_, Jul 01 2022