I’m coming from After Effects and love the possibility to set the particles emitted per frame a lot more than the distribution over time in blender. Is it possible to create a burst of particle that slowly dies out in blender with only one particle system? setting the particles per frame even with bezier curves is very nice in AE, I would kill for this feature in blender.
I don’t think you can do it with one particle system. The particles flow pretty steadily from start to end, and you can’t put a driver on the number of particles to change it during an animation. You CAN add multiple systems to a single object and have them go off in series to create the same effect though.
damned, I hoped adding something like a driver would be possible. I’ll go the adding-additional-systems-route then, thanks for your reply.
Particle systems are pretty easy on computer resources, so combining multiple systems offers some added flexibility in what you can do. I did something similar to what you want with just two systems and a noise modifier to drive the emissions. Can’t remember offhand how I did it but I’ll dig it up and see.
I’m very interested in things even losely resembling some driver thingy for the particles 
You can do it with particles textures.
In a BW image influencing Time setting, black pixels means where particles are emitted at start frame of emission, white pixels at end of emission and levels of grey will correspond to in-betweens.
So, to vary density through time, you just need to cover a smaller area or an higher area for corresponding level of grey.
I was able to get a single emitter to do something like you wanted, using boids, which are easier to manipulate.
What I did was put keyframes on the Lifetime value, starting at about 50 and reducing it to 0 over the length of the animation. I had to play with the start/end values for the emission to balance the effect and get it to look like a burst that fades slowly, or else they tended to appear to implode at the end.
I’ve also played around with fluid particles to get a burst of particles that lingered in the air and slowly faded like a cloud of smoke, for my tank cannon. I had to play with the Drag and Damping values to do it, but it wasn’t difficult.
Thanks for your input. I’ll try both variants. I hope the texture one works like outofthebox as I have a vague idea how to do it. Boids sure look interesting thanks for that piece of info, I’ll investigate 