OFFSET
1,3
COMMENTS
Exponential reversion of A000240 (rencontres numbers).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..400
FORMULA
a(n) = (n-1)! * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * n^(n-k-1) / (n-k-1)!.
MATHEMATICA
nmax = 21; CoefficientList[InverseSeries[Series[x Exp[-x]/(1 - x), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
Table[(n - 1)! Sum[(-1)^k Binomial[n, k] n^(n - k - 1)/(n - k - 1)!, {k, 0, n - 1}], {n, 1, 21}]
Table[HypergeometricU[1 - n, 2, n], {n, 1, 21}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 22 2020
STATUS
approved