WAS IT A CAT I SAW? - 3rd PUZZLE - INCOMPLETE SOLUTION

43132

Ok, but how do we get to this number? Now it's your turn, because your solution is probably better than mine!
I haven't been able to find a simple formula for this one, not even with an ellipsis (dot-dot-dot). If you are able to find a closed-form solution, please e-mail it to me (walter at waltertross × com), and I will publish it here together with your name or pseudonym.

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