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 A373196 #22 Jun 29 2024 16:42:54
%S A373196 1,1,2,17,444,66559954,14648786369948422,
%T A373196 791540878703169050660325841979096789557779,
%U A373196 1918013047695258943191946313451491492494186620117241479813740479213857275772347178176158
%N A373196 Maximal coefficient (in absolute value) in the numerator of C({1..n},x).
%F A373196 C({s},x) = Sum_{i in {s}} (C({s}-{i},x)*x^i)/(1 - Sum_{i in {s}} (x^i)) with C({},x) = 1.
%e A373196 C_x({1,2,3},x) = (-x^15 - 5*x^14 - 12*x^13 - 17*x^12 - 11*x^11 + 4*x^10 + 16*x^9 + 10*x^8 - 6*x^6)/(x^15 + 4*x^14 + 7*x^13 + 4*x^12 - 8*x^11 - 18*x^10 - 13*x^9 + 7*x^8 + 19*x^7 + 11*x^6 - 6*x^5 - 10*x^4 - 2*x^3 + 3*x^2 + 2*x - 1) with maximal coefficient abs(-17) in the numerator, so a(3) = 17.
%o A373196 (PARI)
%o A373196 C_x(s)={my(g=if(#s <1,1, sum(i=1,#s, C_x(s[^i])*x^(s[i]))/(1-sum(i=1,#s, x^(s[i]))))); return(g)}
%o A373196 a(n)={vecmax(abs(Vec(numerator(C_x([1..n])))))}
%Y A373196 Cf. A107429, A114536, A278567.
%K A373196 nonn
%O A373196 0,3
%A A373196 _John Tyler Rascoe_, Jun 28 2024