The given number series is 1, 3, 10, 21, 64, 129, 356, 777.

To find out the wrong number, we need to identify the pattern followed by the numbers in the series.

Pattern:
Let's analyze the given series step by step to identify the pattern:

- The first number, 1, can be obtained by multiplying 1 with itself and adding 0, i.e., (1*1) + 0 = 1.
- The second number, 3, can be obtained by multiplying 2 with itself and adding 1, i.e., (2*2) + 1 = 3.
- The third number, 10, can be obtained by multiplying 3 with itself and adding 1, i.e., (3*3) + 1 = 10.
- The fourth number, 21, can be obtained by multiplying 4 with itself and adding 1, i.e., (4*4) + 1 = 21.
- The fifth number, 64, can be obtained by multiplying 5 with itself and adding 4, i.e., (5*5) + 4 = 29.
- The sixth number, 129, can be obtained by multiplying 6 with itself and adding 5, i.e., (6*6) + 5 = 41.
- The seventh number, 356, can be obtained by multiplying 7 with itself and adding 5, i.e., (7*7) + 5 = 54.
- The eighth number, 777, can be obtained by multiplying 8 with itself and adding 5, i.e., (8*8) + 5 = 69.

From the above analysis, we can observe that the pattern followed by the numbers is as follows:

- For the odd-indexed numbers (1st, 3rd, 5th, 7th), we need to multiply the index with itself and add 1 to get the number.
- For the even-indexed numbers (2nd, 4th, 6th, 8th), we need to multiply the index with itself and add 4 to get the number.

Identifying the wrong number:
By applying the above pattern, we can see that all the numbers in the given series can be obtained correctly except for the sixth number, 129. According to the pattern, the sixth number should be (6*6) + 5 = 41, but it is given as 129 in the series.

Therefore, the wrong number in the given series is 129, which is option 'A'.