Be interesting to see if the father or mother (or a relation) registered the birth.
That is an important point - often the most crucial part of a birth certificate when you are interpreting it is what is in the informant column ( and of course you can't see that in the index at all).
Thanks, Antony and Jon for your insight. I was considering ordering the certificate even before I'd checked the GRO Index, to see what information it contained. I first knew of the child's existence when I came across the parish register entry of his burial. His parents weren't named on that. The search for his identity was complicated by his age at 1841 census being wrongly transcribed as 5 years instead of 5 months. He was with his teenage mother, maternal grandparents + youthful aunts & uncles, but with inaccurate ages for mother & son and no relationships shown on census it wasn't apparent at first who he was. Meanwhile the baby's father was with his older female relative (possible mother) and a work colleague at another address. The couple were witnesses at a wedding the same month, so their relationship seemed to be continuous. I suspect parental opposition to the marriage from the girl's family at least, since they eventually married in 1843, in the month she turned 21, witnesses being groom's friend & friend's fiancée.
The baby died in the summer of 1841, a few weeks after he'd been recorded on the census. His death is indexed under his mother's maiden name. GRO has his age at death as 5, instead of 5 months.