[seqfan] Cute interpretation of A002294

Allan Wechsler acwacw at gmail.com
Wed Aug 9 03:29:10 CEST 2023

According to the Wikipedia article about "Bring radicals", (plus a tiny bit
of elementary algebra),
the generating function for A002294 is the inverse function of f(x) = x^5 +
x. I can't see this mentioned anywhere in the A002294 entry, but perhaps
I'm being blind, and I would appreciate another pair of eyes
double-checking me before I add it.

If you adjoin this generating function to the usual toolkit of addition,
subtraction, multiplication, division, and exponentiation, then, pace the
Abel-Ruffini theorem, you *can* construct a quintic formula, with which any
quintic can be solved. (Of course the formula is disastrously complicated.
I have not seen it written out.)

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