How to find the coefficient

What will be the coefficient of $x^{113}$ in

$(x^{9}+x^{8}+x^{7}+x^{6}+2 x^{5}+2 x^{4}+2 x^{3}+2 x^{2}+2x+3)^{17}$ ?

Please explain, how the answer was obtained.

#Algebra #Combinatorics #Polynomials #PolynomialCoefficients

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

Comments

@Calvin Lin @Sreejato Bhattacharya @Krishna Ar @Michael Mendrin @Michael Tang @Aditya Raut @Sharky Kesa @Finn Hulse @Josh Speckman @Jon Haussmann @Joel Tan @josh silverman

Sorry if anyone feels offended, but I need a way to know this.

Even a wiki article which might help to solve this will help.

Ashu Dablo - 6 years, 7 months ago

Have you studied generating functions?

Finn Hulse - 6 years, 7 months ago

just a little.

Ashu Dablo - 6 years, 7 months ago

@Ashu Dablo – I think you should do some research on partition integers and generating functions, and then look back at the problem.

Finn Hulse - 6 years, 7 months ago

@Finn Hulse – hey finn- could you suggest some useful sources for me to learn about them??

Ashu Dablo - 6 years, 7 months ago

@Ashu Dablo – I'm taking a class called Combinatorial Mathematics.

https://www.edx.org/course/tsinghuax/tsinghuax-60240013x-combinatorial-3771#.VE6id4e0a-I

Finn Hulse - 6 years, 7 months ago

I think this note could help you friend.... Polynomial Expansions

There's a last point in it which i forgot to write, I'll write it soon :P

Aditya Raut - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$