template<int Val>
struct factorial: std::integral_constant<int, Val * factorial<Val - 1>>{};

template<>
struct factorial<0>: std::integral_constant<int, 1>{};

constexpr int factorial(int val)
{
    if(val == 0) {
        return 1;
    }
    else {
        return val * factorial(val - 1);
    }
}

#include <utility>
#include <iostream>

template <std::size_t Zero, std::size_t... Vals>
int constexpr fact_impl(std::index_sequence<Zero, Vals...>)
{
    return (... * Vals);
}


template <std::size_t Val>
int constexpr factorial() { return fact_impl(std::make_index_sequence<Val>{}); }

int main()
{    
    std::cout << factorial<5>() << "\n";
}

S>#include <utility>
S>#include <iostream>

S>template <std::size_t Zero, std::size_t... Vals>
S>int constexpr fact_impl(std::index_sequence<Zero, Vals...>)
S>{
S>    return (... * Vals);
S>}


S>template <std::size_t Val>
S>int constexpr factorial() { return fact_impl(std::make_index_sequence<Val>{}); }

S>int main()
S>{    
S>    std::cout << factorial<5>() << "\n";
S>}
S>

Только факториал пяти равен 120, а не 24 А попытка получить факториал от единицы или нуля у тебя приводит к ошибке компиляции.

Исправленная версия:

template <std::size_t... Vals>
int constexpr fact_impl(std::index_sequence<Vals...>)
{
    return (1 * ... * (Vals + 1));
}

template <std::size_t Val>
int constexpr factorial() { return fact_impl(std::make_index_sequence<Val>{}); }

template <std::size_t... Vals>
int constexpr fact_impl(std::index_sequence<0, Vals...>)
{
    return (1 * ... * Vals);
}

template <std::size_t Val>
int constexpr factorial() { return fact_impl(std::make_index_sequence<Val + 1>{}); }

template <size_t N, typename = std::make_index_sequence<N+1>>
struct Factorial;

template <size_t N, size_t...V>
struct Factorial<N, std::index_sequence<0, V...>> : std::integral_constant<size_t, (1 * ... * V)> {};

int main()
{
    std::cout << Factorial<0>::value << std::endl;
    std::cout << Factorial<1>::value << std::endl;
    std::cout << Factorial<2>::value << std::endl;
    std::cout << Factorial<3>::value << std::endl;
    std::cout << Factorial<4>::value << std::endl;
    std::cout << Factorial<5>::value << std::endl;
}