Gauss as a kid was into triangular numbers a lot. He made many theories . Probably he made this one too.
Three consecutive numbers of my type and its reciprocal both give triangular numbers.
See below
It is a decent knock on the door of Abel Prize committee.
I am thankful to Gauss for that.
The above equation gives weight to my theory as well.
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So the function of finite sigma of 2n!/(2n-1)!-n!/(n-1)! gives triangular numbers.
Then the above gives triangular numbers.
And the sum of above is the number system.
I get a feeling that these are of golden ratio, antonyms, verbal talks.
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