DouKaku?

#include <iostream>
#include <vector>
typedef unsigned int bit_t;

std::vector<bit_t> bits;
int n, n2, cnt = 0;

void comb(int a, int k, int s, bit_t b) {
  if (k < n-1)
    for (int i = a; i < n2; ++i)
      comb(i+1, k+1, s-i, b | 1 << (i-1));
  else
    if (a <= s && s <= n2)
      bits.push_back(b | 1 << (s-1));
}

void calc(int s, int k, bit_t b) {
  if (k == n) { ++cnt; return; }

  for (int i = s; i < (int)bits.size(); ++i)
    if (!(b & bits[i]))
      calc(i+1, k+1, b | bits[i]);
}

int main() {
  n = 5;
  n2 = n * n;
  int m = n * (n2+1) / 2;

  comb(1, 0, m, 0);
  calc(0, 0, 0);

  std::cout << cnt << std::endl;
}