Question

What is the Pascal triangle up to 30 rows?

Answer 1

The `30th` row can be represented through the constant coefficients in the expanded form of `(x+1)^30`:

`x^30+30 x^29+435 x^28+4060 x^27+27405 x^26+142506x^25+593775 x^24+2035800 x^23+5852925 x^22+14307150 x^21+30045015 x^20+54627300 x^19+86493225 x^18+119759850 x^17+145422675 x^16+155117520 x^15+145422675 x^14+119759850 x^13+86493225 x^12+54627300 x^11+30045015 x^10+14307150 x^9+5852925 x^8+2035800 x^7+593775 x^6+142506 x^5+27405 x^4+4060 x^3+435 x^2+30 x+1`

http://www.wolframalpha.com/input/?i=%28x%2B1%29%5E30

Here's an interactive website:

http://mathforum.org/dr.cgi/pascal.cgi?rows=30