The generic instance on the Nucelo-F401RE is on USART2.
That's why Serial2 is defined and mapped on Serial.

If you want another serial, you can add a build_opt.h file with: -DENABLE_HWSERIAL1
This will define the Serial1 using the first USART1 instance found in the PeripheralPins.c.
In this case on PA10/PA9.
https://github.com/stm32duino/Arduino_Core_STM32/blob/master/variants/NUCLEO_F401RE/PeripheralPins.c#L153
https://github.com/stm32duino/Arduino_Core_STM32/blob/master/variants/NUCLEO_F401RE/PeripheralPins.c#L142

One other option is to simply define it:
HardwareSerial Serial1(PA10, PA9);
or
HardwareSerial Serial1(PB7, PB6);
...

So your code can be:

long val = 0;
HardwareSerial Serial1(PA10, PA9);

void setup() {
  Serial1.begin(115200); 
}

void loop() {
  // put your main code here, to run repeatedly:
  val++;
  Serial1.write(val);
 
  delay(100);
}

Thank you so much Frederic for the help, now I see my question was very trivial!

I think this issue is natural for an Arduino user, I have faced it myself some weeks ago.
Maybe we should document it clearly somewhere.
Maybe here: https://github.com/stm32duino/wiki/wiki/API

Yes, documenting it would help a lot for new unexperienced users just like me

You're right guys, several documentation are missing.
I've planned to use the GitHub page feature to documents the core but time is always the missing ingredients. 😭

Roger has created https://github.com/stm32duino/stm32duino.github.io
This would be fine to use it. Then all will be available thanks http://stm32duino.github.io

Ok nice, I can't promise but I might help a bit to kick start the doc.
So you would advise to use the plain website instead of the wiki?
Because I am not a web developer, I am Ok to write down some markdown, but not much to write plain HTML and CSS...
Or maybe we can find a nice documentation template for a static website generator like jekyll or hugo.

Honestly, I don't know. Maybe a new issue can be opened to discuss about that and maybe some users could share their feedback about GitHub pages usage.