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A293116
Expansion of e.g.f. exp(x/(x-1)).
11
1, -1, -1, -1, 1, 19, 151, 1091, 7841, 56519, 396271, 2442439, 7701409, -145269541, -4833158329, -104056218421, -2002667085119, -37109187217649, -679877731030049, -12440309297451121, -227773259993414719, -4155839606711748061, -74724654677947488521
OFFSET
0,6
LINKS
Geoffrey B. Campbell, Visible Point Vector Partition Identities for Hyperpyramid Lattices, arXiv:2309.16094 [math.CO], 2023. See pp. 14, 27.
FORMULA
E.g.f.: exp(x/(x-1)).
a(n) = (-1)^n * A111884(n).
E.g.f.: Product_{k>=1} (1 - x^k)^(phi(k)/k), where phi() is the Euler totient function (A000010). - Ilya Gutkovskiy, May 25 2019
D-finite with recurrence a(n) +(-2*n+3)*a(n-1) +(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Mar 13 2023
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, -add(
a(n-j)*binomial(n-1, j-1)*j!, j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Sep 30 2017
MATHEMATICA
CoefficientList[Series[E^(-x/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2017 *)
PROG
(PARI) my(x='x+O('x^66)); Vec(serlaplace(exp(x/(x-1))))
CROSSREFS
Column k=0 of A293119.
Sequence in context: A153692 A142060 A125356 * A066668 A111884 A126514
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 30 2017
STATUS
approved