How do I use factorial (!) in a vega formula transform - vega-lite

Question

I am trying to create a histogram of a binomial distribution PMF using a vega js specification.
How is this usually done? The vega expressions does not include functions for choose, or factorial, nor does it include a binomial distribution under the statistical functions.
I also cannot seem to reference other functions within the vega specification (i.e. for yval below).
"data":[
{"name": "dataset",
"transform": [
{"type":"sequence", "start": 1, "stop": 50, "step": 1, "as": "seq" },
{"type": "formula", "as": "xval", "expr": "if(datum.seq<nval,datum.seq,NaN)"},
{"type": "formula", "as": "yval", "expr": "math.factorial(datum.xval)
" }
]}],
Thanks.

Answer 1

There is no factorial operation available, but one suitable option might be to approximate it with Stirling's approximation, or perhaps a Stirling series if more accuracy is required.
For example, in Vega-Lite (view in editor):
{
"data": {
"values": [
{"n": 0, "factorial": 1},
{"n": 1, "factorial": 1},
{"n": 2, "factorial": 2},
{"n": 3, "factorial": 6},
{"n": 4, "factorial": 24},
{"n": 5, "factorial": 120},
{"n": 6, "factorial": 720},
{"n": 7, "factorial": 5040},
{"n": 8, "factorial": 40320},
{"n": 9, "factorial": 362880},
{"n": 10, "factorial": 3628800}
]
},
"transform": [
{
"calculate": "datum.n == 0 ? 1 : sqrt(2 * PI * datum.n) * pow(datum.n / E, datum.n)",
"as": "stirling"
},
{"fold": ["factorial", "stirling"]}
],
"mark": "point",
"encoding": {
"x": {"field": "n", "type": "quantitative"},
"y": {"field": "value", "type": "quantitative", "scale": {"type": "log"}},
"color": {"field": "key", "type": "nominal"}
}
}