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Let $f(n)$ be an arbitrary function such that $f(n)\in\mathbb{Z}$. Let $$ F(x)=\sum\limits_{m\geqslant 0}f(m)x^m $$ Define the operator $\operatorname{SR}$, which is associated with the series revers …

Let $a(n)$ be A258173 i.e. sum over all Dyck paths of semilength $n$ of products over all peaks $p$ of $y_p$, where $y_p$ is the $y$-coordinate of peak $p$. A Dyck path of semilength $n$ is a $(x,y) …

Let $a(n,p,q)$ be the family of integer sequences such that ordinary generating functions for it are $\frac{1}{G_1(0,x)}$ where $G_1(0,x)$ are continued fractions such that $$ G_1(j,x)=1-\cfrac{(qj+1 …

Let $a(n)$ be A088352. Here $a(n)$ is an integer sequence with generating function $A(x)$ such that $$ A(x) = \cfrac{1}{1-x-\cfrac{x^2}{1-x^3-\cfrac{x^4}{1-x^5-\cfrac{x^6}{1-x^7-\cfrac{x^8}{\ddots}}} …

Please note that this question has been completely reworked in order not to overload it with unnecessary and useless information. Let $f(n)$ be an arbitrary function with integer values. Let $a(n)$ b …