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New posts in generating-functions
What is the number of squares in $S_n$?
group-theory
finite-groups
permutations
generating-functions
symmetric-groups
Coefficient of $\frac{1}{1-x-x^2-..-x^{d-1}}$ and its asymptotic
combinatorics
asymptotics
recurrence-relations
generating-functions
combinatorial-proofs
Is it possible, solely with the function $f(x) = \sum_{n>0} a_nx^n$, to obtain the function $\sum_{n>0} \frac{a_n}{n!} x^n$?
real-analysis
generating-functions
laplace-transform
Binomial Coefficient
binomial-coefficients
generating-functions
inverse-function
Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$
combinatorics
summation
binomial-coefficients
generating-functions
Words built from $\{0,1,2\}$ with restrictions which are not so easy to accomodate.
combinatorics
generating-functions
formal-languages
Poisson distribution with exponential parameter
probability
probability-distributions
generating-functions
Why is it important to have the closed form of a generating function?
combinatorics
generating-functions
Identity with Harmonic and Catalan numbers
sequences-and-series
generating-functions
harmonic-numbers
catalan-numbers
Using generating functions find the sum $1^3 + 2^3 + 3^3 +\dotsb+ n^3$
discrete-mathematics
generating-functions
Important identities that can be obtained by manipulating the function $\frac{x}{e^x-1} = \frac{B_0}{0!} + \frac{B_1}{1!}x + \frac{B_2}{2!}x^2 + ...$?
calculus
complex-numbers
power-series
intuition
generating-functions
Deriving the asymptotic estimate (9.62) in Concrete Mathematics
discrete-mathematics
recurrence-relations
asymptotics
generating-functions
Show that $\sum_{k=1}^n \binom{n}{k}k^2=n^2\cdot \:2^{n-2}+n\cdot \:2^{n-2}$.
combinatorics
generating-functions
binomial-theorem
Power series expansion of $\arctan{\left(\frac{1-x^2}{2+x^2}\right)}$
sequences-and-series
power-series
generating-functions
Bernoulli numbers generating function
number-theory
generating-functions
bernoulli-numbers
Generalized Harmonic Number Summation $ \sum_{n=1}^{\infty} {2^{-n}}{(H_{n}^{(2)})^2}$
real-analysis
sequences-and-series
generating-functions
harmonic-numbers
Why would you take the logarithmic derivative of a generating function?
combinatorics
generating-functions
oeis
Integral Representation of Infinite series
combinatorics
analysis
special-functions
generating-functions
residue-calculus
Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$
combinatorics
discrete-mathematics
generating-functions
combinatorial-proofs
catalan-numbers
Harmonic Numbers series I
sequences-and-series
generating-functions
closed-form
catalan-numbers
harmonic-numbers
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