This paper suggests that one 20 year old tree will sequester 1 tonne of Carbon which is 3.67 tonnes of CO2 which is roughly a year's CO2 footprint of one UK person or a third of a US person.
However, your question is about planting one tree, which is subtly different.
In order to get a decent healthy twenty year old tree, you need to plant about twelve trees of various species, relatively close together, so that they all grow straight upwards. Young trees require less space than older larger trees, so they can be closer together, and then progressively cut them down over a ten to twenty year period so that one remains and can grow for over a hundred years. Mixed-species forests are less susceptible to pests and disease than mono-culture forests.
I guess its a philiosophical point. If you are operating a carbon sequestration business to maximise the CO2 in the trees, then you could have a mono-culture plantation, of the most CO2 dense wood, and use pesticides and surgical culling to prevent the any infection wiping out the whole site, and have that as a business expense.
On the other hand if you are merely trying to reforest a bit a wasteland and rebuild a country's ancient woodland, then you'll have a mixed species plantation with a broader community of wildlife that keep pests in check with a huge complex ecology of prey and predator curves, and many diverse native tree and shrub species, and try not to introduce invasive and non-native species. It wouldn't optimise CO2 sequestration, but it would be more sustainable and ecologically 'better'.
I'm afraid I don't know the details of the UN's 11 billion tree plan, but it could end up being 11 billion trees planted, but after twenty years only 1 billion remain.
There's also another element which needs to be understood, whilst a twenty year old tree might sequester one tonne of Carbon in its woody mass, it has over its lifespan photosynthesized a load more oxygen, and sequestered Carbon in leaves which are dropped each year. Whilst the carbon in the leaves does return to the atmosphere when they break down and decay, that amount of carbon is tied into a cycle of being in the air, then in leaves, then breaking down, and returning to the air. The more leaves there are, the more carbon is in that cycle rather than just building up in the atmosphere.
Our one tonne tree, in any one year might have a tonne of CO2 sequestered in its leaves, and two tonnes sequestered in the dead leaves at its base and three tonnes of CO2 in the air released from dead leaves waiting to be the next years new leaves. If the tree didn't exist, that CO2 would just be in the air.
Even the other trees that are culled will be sequestering CO2 and expiring Oxygen during their shorter lifespans. But this is harder to measure.