Slightly faster. It's getting too silly, though. However, the step function is getting smaller due to better understanding of the problem.

// inc_c - http://perlmonks.org/?node_id=1128230
// 8.52 secs. for 16/32 count=601080390 -O2
// 3.08 secs. for 16/32 count=601080390 -O3

#include <stdlib.h>
#include <stdio.h>

#define N 16 // number of elements wanted
#define M 32 // place

static int place[N+1];
static int count = 0;

int
step(void)
  {
  int *p = place;

  for(int i = 0; i < N; *p++ = i++ )
    {
    if(*p < p[1] - 1)
      {
      ++*p;
      return 1;
      }
    }
  return 0;
  }

int
main(int argc, char **argv)
  {
  int i;
  int more = 1;

  for(i = 0; i < N; i++) place[i] = i;
  place[N] = M;

  while( more )
    {
    //for(i = 0; i < N; i++) printf(" %d", place[i]);
    //putchar('\n');
    count++;
    more = step();
    }

  printf("\ncount %d\n", count);

  exit(0);
  }
[download]

Thanks for the opportunity to scrape some rust off my C skills :)