OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..449
FORMULA
G.f.: Sum(n!*(-x)^n/Product(1-x^k, k=1..n), n=1..infinity).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>1,
b(n, i-1), 0)+expand(b(n-i, min(n-i, i))*x))
end:
a:= n-> (p-> add(i!*coeff(p, x, i)*(-1)^i, i=0..n))(b(n$2)):
seq(a(n), n=0..27); # Alois P. Heinz, Sep 18 2019
MATHEMATICA
CoefficientList[ Series[ Sum[ n!(-x)^n / Product[1 - x^k, {k, n}], {n, 0, 22}], {x, 0, 22}], x]
PROG
(Sage)
from sage.combinat.partition import number_of_partitions_length
[sum([(-1)^k*number_of_partitions_length(n, k)*factorial(k) for k in (0..n)]) for n in (0..22)]
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Aug 01 2015
STATUS
approved