25 problems

Let $E=E(a,b,c,d)$ be the elliptic curve … with nonzero discriminant, and let $(0,0)$ be the reference point. Let $h_n$ be the Hankel transform above and let $h_n^*$ denote the ass…

Somos 4 conjecture. The Hankel transform of the expansion of $f(x)/x$ is a

Higher Hankel transform degree conjecture. The sequence

Let $E=E(a,b,c,d)$ be the elliptic curve … with nonzero discriminant, and let $(0,0)$ be the reference point. Let $h_n$ be the Hankel transform of the sequence generated by … where…

Let $h_n$ be the Hankel transform of the Rueppel sequence $r_n$, and let $H_n$ be the Hankel transform of the once-shifted Rueppel sequence $r_{n+1}$. A268411 product conjecture. T…

A088748 Hankel-transform conjecture. The even-indexed Hankel-transform terms satisfy

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be the sequence of determinants of successive Hankel matrices. A005811 Hankel-transform…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be the sequence of determinants of successive Hankel matrices. A005811 Hankel-transform…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be reduced termwise modulo $2$. Modulo-2 periodicity conjecture. The Hankel transform of…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform of a sequence be the sequence of determinants of its successive Hankel matrices. Periodi…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform of a sequence be the sequence of determinants of its successive Hankel matrices. Rueppel…

Robbins-number conjecture. The Hankel transform of this revert transform is the Robbins number sequence

Hankel-transform square conjecture. This Hankel transform is

Let $a$ and $b$ be parameters, let $m$ be a shift, and consider the sequence $aC_{n+m}+bC_{n+m+1}$. In the case $m=2$, the successive principal minors of the associated continued-f…

General Hankel-transform conjecture. The Hankel transform is given by

Let $a$ and $b$ be parameters, let $m$ be a nonnegative integer, and let $C_n$ denote the $n$th Catalan number. For the Hankel transform of the sequence $aC_{n+m}+bC_{n+m+1}$, the…

Structured discrete Hankel-transform conjecture. The following pairs are feasible:

Discrete Hankel-transform feasibility conjecture. If $(k,q)$ is $(s,\nu)$-feasible, then $(k+1,q)$ and $(k,q-1)$ are $(s,\nu)$-feasible. The function…

General Somos 4 conjecture. The Hankel transform is an $(\alpha,\beta)$ Somos $4$ sequence, where

Let $a_n$ be the sequence with generating function … where $c(x)$ is the Catalan generating function. Specialized elliptic-curve Somos 4 conjecture. The Hankel transform of $a_n$ i…

Let $c(x)$ denote the Catalan generating function and define a sequence by … Define … … Cubic-family Hankel-transform conjecture. The Hankel transform of the sequence with generati…

Let $a_n(\beta)$ be defined by … with $a_0=1$, $a_1=0$, and $a_2=\beta$, and let $h_n(\beta)$ be its Hankel transform. Recurrence-form Hankel-transform conjecture. The Hankel trans…

Let $a_n(p,q,r,s,t)$ be the five-parameter generalized Catalan sequence. Assume … Specialized generalized Catalan Somos 4 conjecture. The Hankel transform of $a_n(p,q,1,q-p+1,1)$ i…

Let $a_n(p,q,r,s,t)$ be the five-parameter generalized Catalan sequence and let $h_n$ denote the Hankel transform of $\frac{1}{p}a_{n+1}(p,q,r,s,t)$. A $(\alpha,\beta)$ Somos $4$ s…

Barry's conjecture. The Hankel transform of $(a_n)$ consists solely of the numbers $-1$, $0$, and $1$, and its non-zero terms occur at locations indexed by $(b_n)$. Conversely, giv…