(* Series from Campostrini 2001, https://oeis.org/A002913/b002913.txt *)

chin={1,6,30,150,726,3510,16710,79494,375174,1769686,8306862,38975286,182265822,852063558,3973784886,18527532310,86228667894,401225368086,1864308847838,8660961643254,40190947325670,186475398518726,864404776466406,4006394107568934,18554916271112254,85923704942057238};

chiHT[T_]=Sum[chin[[p]]Tanh[1/T]^(p-1),{p,Length[chin]}];

Plot[chiHT[T],{T,4,10},PlotRange->{0,20}]

Rats=Drop[chin,-1]/Drop[chin,1]//N

Jc=0.221654626; vc=Tanh[Jc] (* Ferrenberg 2018 *)

dnRats=Table[n*Rats[[n]]-(n-1)*Rats[[n-1]],{n,2,Length[Rats]}]//N

avRats=Table[(dnRats[[n]]+dnRats[[n+1]])/2,{n,1,Length[dnRats]-1}]

exactvc=Table[vc,{n,Length[Rats]}];

ListPlot[{Rats,dnRats,avRats,exactvc},Joined->True,PlotRange->{0.20,0.23}]

dLogChi[T_]=D[Log[chiHT[T]],T];

Tc=1/Jc

gamma=1.237075;

Plot[{(Tc-T)*dLogChi[T],gamma},{T,4,10},PlotRange->{-0.6,1.6}]