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Given $(2x^2+3x+4)^{10}=\sum_{r=0}^{20}a_rx^r$ Find $\frac{a_7}{a_{13}}$

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#combinatorics #binomial-coefficients #factorial
53
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Diophantine with primes factorials

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#prime-numbers #diophantine-equations #factorial
37
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Can someone explain how does step 1 render to step 2?

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#induction #factorial #factoring
108
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Factorial representation with sum of products

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#algorithms #factorial #computational-mathematics
1.6k
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Factorials and prime numbers

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#elementary-number-theory #prime-numbers #divisibility #factorial
826
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Laplace approximation of Poisson posterior from MacKay

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#calculus #probability #factorial #gamma-function #laplace-method
82
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Minimum of maximum with factorial

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#optimization #asymptotics #factorial #nonlinear-optimization #maxima-minima
95
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Double sum factorial manipulation

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#algebra-precalculus #summation #factorial
249
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Find the largest integer $k$ for which $3^k$ divides $400 \choose 200$.

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#number-theory #combinations #factorial
140
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Moment generating function (find the probability)

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#probability #statistics #factorial #moment-generating-functions
88
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Proof of inverse factorial decomposition $\frac{1}{n!}=\sum\limits^n_{i=1}\frac{(-1)^{n+i}}{(i-1)!(n+1-i)!}$

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#probability #combinatorics #number-theory #factorial
60
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$\prod$ and factorial

Published on
#factorial
372
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Factorial$(kn)!$ expansion

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#calculus #linear-algebra #discrete-mathematics #factorial
90
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How is it that (p-1)! is not congruent with 0 mod p if p is prime?

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#prime-numbers #modular-arithmetic #factorial
130
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Proving a limit for factorials

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#factorial #gamma-function

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