R Under development (unstable) (2015-09-06 r69303) -- "Unsuffered Consequences"
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> ## Example in which the fit for the null deviance fails to converge:
> # https://stat.ethz.ch/pipermail/r-help/2012-May/313161.html
> Y <- c(rep(0,35),1,2,0,6,8,16,43)
> beta <- 42:1
> cst <- lchoose(42, beta)
> tau <- (beta^2)/2
> fit <- glm(formula = Y ~ offset(cst) + beta + tau, family = poisson)
Warning messages:
1: glm.fit: algorithm did not converge 
2: In glm(formula = Y ~ offset(cst) + beta + tau, family = poisson) :
  fitting to calculate the null deviance did not converge -- increase 'maxit'?
> 
> proc.time()
   user  system elapsed 
  0.077   0.014   0.081