I have been searching an integer sequence in OEIS. The sequence is the following: OEIS A321234 (https://oeis.org/A321234) . So far, so good. However, this sequence is the denominator of a Hypergeometric Series, the following one:
$${}_3 F_2([1/2, 1, 1], [3/2, 3/2], x).$$
The problem is: I do not even know what those kind of series are. Do not even know what this notation means. Could someone recomend me any book references so as to understand it better? I have read Wiki's page, but it seems not enough.
Thanks a lot
$$\, _3F_2\left(\frac{1}{2},1,1;\frac{3}{2},\frac{3}{2};x\right)$$ is one of the many hypergeometric functions (google for that).
They are very special functions corresponding to infinite sums. For this one, the first terms of its expansion are $$1+\frac{2 x}{9}+\frac{8 x^2}{75}+\frac{16 x^3}{245}+\frac{128 x^4}{2835}+\frac{256 x^5}{7623}+\frac{1024 x^6}{39039}+\frac{2048 x^7}{96525}+\frac{32768 x^8}{1859715}+O\left(x^{9}\right)$$
You would find the numerators in sequence $A046161$