This recursion came up in my calculations and it turned out to have a nice simple closed form. #math #algebrapic.twitter.com/sqV51JBWY6
Was hoping you’d post the closed form.. now I guess I have to solve it
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Coefficients are Stirling numbers of the first kind (0 < k < n). - sum_{k=1}^{n-1} [n;k] * x^k Proof is via recurrence relation [n;k] + n[n;k+1] = [n+1;k+1], [n;n] = 1; [n;0] = 0. (I entered a few coefficients into http://oeis.org for a hint)
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Seems to me it's simply: P_n = x^n – x(x+1)(x+2)…(x+n-1)
End of conversation
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