Summing up array elements using OpenMP is not working correctly for large arrays (C)

I wanted to use OpenMP around a for-loop that basically sums up the array elements. For comparison, I also sum up the array elements in a serial fashion. For large array-sizes, array_size>=5795, the sums are no longer equal.

This is the OpenMP-parallelized loop:

#pragma omp parallel for reduction(+:parallel_sum)
    for (i = 0; i < array_size; i++) {
        parallel_sum += array[i];
    }

And this is the full code:

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

int main() {
    float          *array, serial_sum, parallel_sum;
    size_t          array_size, i;

    serial_sum   = 0.;
    parallel_sum = 0.;

#pragma omp parallel
    printf( "number of threads used in parallized part: %d\n", omp_get_num_threads());

    printf("enter size of array\n");
    scanf("%zu", &array_size);

    // memory allocation
    array = (float *) malloc(sizeof(float) * array_size);

    // initialize array
    for (i = 0; i < array_size; i++)
        array[i] = i;

    // calculate the array sums, parallel first, then serial
#pragma omp parallel for reduction(+:parallel_sum)
    for (i = 0; i < array_size; i++) {
        parallel_sum += array[i];
    }

    for (i = 0; i < array_size; i++)
        serial_sum = serial_sum + array[i];

    if (serial_sum == parallel_sum)
        printf("\nserial and parallel sums are equal\n");
    else
        printf("\nserial and Parallel sums are NOT equal\n");

    // free memory
    free(array);

    return 0;
}

Since the sum can be easily calculated by hand using the sum-formula by Gauss, sum = (n^2+n)/2, where n corresponds to array_size, both sums are wrong... I guess I am having some memory issues then...?