Ah ha! A subject near and dear to my own little black heart! Not sure how many songs have been sung by the Count himself, but here's some to get you started.
1 The name of the song you remember is "The Batty Bat".
The following are from a VCD of songs I got from my deals with Justin.
2 The Song of the Count.
3 Knick-Knack Paddywhack.
4 My First Day of School.
5 Count Up to 9.
6 Eight Beautiful Notes.
7 My Transylvania Tootsie.
8 Not sure what it's name is, but there's a song where the Count goes to the market and ends up counting potatoes, umbrellas, and newspapers.
9 Not sure what the name of it is, but there's a sweet song that could be considered "The Count's Lullaby", a song he sings for all his pets to go to sleep.
10 Not exactly a song sung by him, but there are the spoken inserts during the song "It's Been a Long Long Time".
That's 2 Longs and 1 Time!
11 The song he sang about what a person can do with their hands, his favorite part of the body because of counting all those things.
12 Not exactly a song sung by him, but he did appear along with Reporter Kermit at one moment during the video for the song "40 Blocks from my School".
13 The Transylvania Polka part of one of the Sesame Street Live shows from the 80's, I believe it's the one of the Case of the Missing Bird where Big Bird's hoodwinked into showbuisness by PT Barnswallow.
Hope this is enough and have a vonderful night!