Help with std::accumulate

[zotan]

Hello friends, I'm wanting to translate the following code using td::accumulate, but I'm still confused with the syntax. Here is he code:

unsigned int binomial(int n, int k) {

	std::vector<unsigned int> S(k + 1, 0u);

	S[0] = 1u;

	for(int i = 1; i <= n; i++) {
		for(int j = std::min(i, k); j > 0; j--)
			S[j] = S[j] + S[j - 1];
	}

	return S[k];
}

unsigned int rank(const std::vector<int> &S) {	
	
	unsigned int r = 0u;
	int k = 1;
	
	for(auto n = S.begin(); n != S.end(); n++, k++){
		r += binomial(*n, k);
	}

	return r;
		
}

How would be the rank function translated to std::accumulate?

	return std::accumulate(S.begin(), S.end(), 0u, [&] // ?(int n) {
	 // ??	return binomial(n, k++); 
	});

[keskiverto]

http://www.cplusplus.com/reference/numeric/accumulate/
States:

Binary operation taking an element of type T as first argument and an element in the range as second, and which returns a value that can be assigned to type T.

and
init = init + *first; // or: init=binary_op(init,*first) for the binary_op version

Does that mean:

[&k] (unsigned int init, int elem)
{
  return init + binomial(elem, k++);
}

[zotan]

Absolutely perfect my friend. Thank you!