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 A355372 #8 Jul 01 2022 00:05:54
%S A355372 0,1,9,77,714,7374,85272,1102968,15908400,254866320,4516084800,
%T A355372 88102382400,1883199024000,43885950595200,1109416142822400,
%U A355372 30273281955302400,887493144729139200,27827941161784780800,929449073791558656000,32943696020637889536000,1234946945823695419392000
%N A355372 Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^3.
%C A355372 Conjecture: For p prime, a(p) == -1 (mod p).
%F A355372 a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062139(n, k + 1).
%F A355372 a(0) = 0, a(n) = n!*Sum_{k=1..n} (n-k+2)*(n-k+1)*(2^k-1)/(2*k).
%F A355372 a(n) = A000292(n)*n!*hypergeom([1 - n, 1, 1], [2, 4], -1). - _Peter Luschny_, Jun 30 2022
%p A355372 A355372 := n -> A000292(n)*n!*hypergeom([1 - n, 1, 1], [2, 4], -1):
%p A355372 seq(simplify(A355372(n)), n = 0..20);
%t A355372 CoefficientList[Series[Log[(1 - x)/(1 - 2*x)]/ (1 - x)^3,{x,0,20}],x]Table[n!,{n,0,20}] (* _Stefano Spezia_, Jun 30 2022 *)
%Y A355372 Cf. A000292, A062139, A355171.
%K A355372 nonn
%O A355372 0,3
%A A355372 _Mélika Tebni_, Jun 30 2022