# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 4, December 2020 pp. 307–315.

Convolution sums with Catalan numbers

**Authors**:
Aeran Kim

**Author institution:**A Private Mathematics Academy, 1-#406, 23, Maebong 5-gil, Deokjin-gu, Chonju, Chonbuk, 54921, Republic of Korea

**Summary: **
In this article we deal with the Catalan number Cn composing
the convolutions sums, for instance,
∑
{k=0}{n} {1}/{n+2-k} C{k} C{n-k},
∑{k=0} [{n}/{2}]4 {k} C{k} C{n-2k},
∑{k=0} [{n}/{3}] 16{k} C{k} C{n-3k},
and etc., and deduce their formulae.

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