JSFiddle - React, Tailwind, and code Playground

HTML

N: <input type="text" id="N" /><br/>
L: <input type="text" id="L" /><br/>
R: <input type="text" id="R" /><br/>

<input type="button" id="go" value="test" />

JavaScript

function g(N, L, R) {
    var acc = 0;
    for (var k=1; k<=N; k++) {
        acc += comb(N-1, k-1) * f(k-1, L-1) * f(N-k, R-1);
//        alert("Pasada "+k+": "+comb(N-1, k-1)+" * "+f(k-1, L-1)+" * "+f(N-k, R-1)+" = "+comb(N-1, k-1) * f(k-1, L-1) * f(N-k, R-1));
    }
    return acc;
}

function f(N, L) {
    if (N==L) return 1;
    else if (N<L) return 0;
    else {
        var acc = 0;
        for (var k=1; k<=N; k++) {
            acc += comb(N-1, k-1) * f(k-1, L-1) * fact(N-k);
        }
        return acc;
    }
}

function comb(n, k) {
    return fact(n) / (fact(k) * fact(n-k));
}

function fact(n) {
    var acc = 1;
    for (var i=2; i<=n; i++) {
        acc *= i;
    }
    return acc;
}

$("#go").click(function () {
    alert(g($("#N").val(), $("#L").val(), $("#R").val()));
});