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Johann Cigler
  • Member for 10 years, 6 months
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9 votes
1 answer
174 views

Proof of a Binomial identity

7 votes
0 answers
290 views

Lucky chance or combinatorial cause?

7 votes
2 answers
611 views

Prove $(1-x)^{2k+1} \sum\limits_{n\ge 0}\binom{n+k-1}{k}\binom{n+k}{k} x^n = {\sum\limits_{j\ge 0} \binom{k-1}{j-1}\binom{k+1}{j} x^j} $

5 votes
0 answers
126 views

An identity for $q-$Fibonacci numbers if $q$ is a root of unity.

4 votes
2 answers
240 views

A curious Hankel determinant

4 votes
1 answer
176 views

A class of integer valued polynomials

3 votes
2 answers
194 views

A Stirling number identity

3 votes
0 answers
70 views

Are these polynomials gamma-nonnegative?

3 votes
0 answers
34 views

Hankel determinants related to Motzkin paths

3 votes
0 answers
103 views

Reference request for some determinants of binomial coefficients

2 votes
0 answers
88 views

Parity of some binomial coefficients

2 votes
1 answer
91 views

A binomial identity related to Lucas polynomials.

2 votes
1 answer
119 views

A determinant of a matrix with binomial coefficients

2 votes
1 answer
89 views

A conjectured identity for generalized Fibonacci polynomials

2 votes
0 answers
116 views

Is there a combinatorial interpretation for the following sum?

2 votes
1 answer
56 views

Congruence properties of $\sum{\binom{n}{k}}^2t^k$ $\mod{(t+1)}.$

2 votes
1 answer
128 views

An interesting limit of certain $q$-binomial sums.

2 votes
1 answer
89 views

Central trinomial coefficient as number of lattice paths

2 votes
1 answer
66 views

Generalized Eulerian polynomials

2 votes
1 answer
90 views

Binomial determinants related to Hoggatt triangles

2 votes
0 answers
130 views

Product representation of the exponential series.

2 votes
1 answer
76 views

A curious infinite product

2 votes
1 answer
64 views

Characteristic polynomials for a class of simple matrices

2 votes
1 answer
57 views

Number of Motzkin paths with no horizontal steps at positive heights

1 vote
0 answers
44 views

Generating functions of Hankel determinants related to Hoggatt triangles

1 vote
0 answers
43 views

Discriminant of q-analogs of positive integers

1 vote
0 answers
51 views

**A curious number triangle.**

1 vote
1 answer
156 views

Convolution of Narayana polynomials

1 vote
1 answer
83 views

Number of $k-$subsets of $ \lbrace 1,2, \ldots ,n \rbrace$ with even sum.

1 vote
0 answers
53 views

An identity for generalized q-Fibonacci polynomials