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5m
revised How many directed graphs of size n are there where each vertex is the tail of exactly one edge?
labelled endofunctions
30m
answered How many directed graphs of size n are there where each vertex is the tail of exactly one edge?
1d
revised How many arrays with crossed cells, order of rows/columns irrelevant
Perl Script III
1d
revised How many arrays with crossed cells, order of rows/columns irrelevant
Perl Script
1d
answered Prove $\sum_{i=0}^{i=x} {x \choose i} {y+i \choose x}+\sum_{i=0}^{i=x} {x \choose i} {y+1+i \choose x}$
2d
answered Sums of binomial coefficients
2d
comment Prove that $\sum_{k=1}^\infty\frac{1}{16k^4 - 1} = \frac{1}{2} - \frac{\pi}{8}\coth(\frac{\pi}{2})$
There is a relevant technique at this MSE link.
Sep
21
revised How many arrays with crossed cells, order of rows/columns irrelevant
vectors
Sep
21
answered How many arrays with crossed cells, order of rows/columns irrelevant
Sep
19
comment Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
(+1) Very nice work.
Sep
19
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
punctuation
Sep
19
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
simple
Sep
18
comment Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
(+1) Good work. The detour via complex variables appears not to be necessary here.
Sep
18
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
integral
Sep
18
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
period
Sep
18
answered Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
Sep
18
comment Evaluating a series to order “three halves”
The remainder is in the left side of the rectangular contour. (The top and bottom contributions vanish as the height goes to $\pm\infty.$) For more information consult "Mellin Transform Asymptotics" by Sedgewick and Flajolet, INRIA Rapport de Recherche 2956, which explains it better than I ever could.
Sep
17
comment Evaluating a series to order “three halves”
It's an asymptotic.
Sep
16
comment Evaluating a series to order “three halves”
Thanks, and good luck.
Sep
16
comment Combinatorial identity on partitions
There are two proofs by different users at this MSE link.