OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial
FORMULA
E.g.f.: series reversion of -log(1 - x) * exp(-x).
a(n) = (n - 1)! * [x^n] exp(n*(1 - exp(-x))).
a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling2(n,k) * n^(k-1).
a(n) = (-1)^n * BellPolynomial_n(-n) / n.
MATHEMATICA
nmax = 21; CoefficientList[InverseSeries[Series[-Log[1 - x] Exp[-x], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
Table[Sum[(-1)^(n - k) StirlingS2[n, k] n^(k - 1), {k, 1, n}], {n, 1, 21}]
Table[(-1)^n BellB[n, -n]/n, {n, 1, 21}]
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(n-k) * stirling(n, k, 2) * n^(k-1)); \\ Michel Marcus, Apr 20 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 20 2020
STATUS
approved