OFFSET
0,3
COMMENTS
1/A(x) is g.f. for A000219.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)
E. M. Wright, Coefficients of a reciprocal generating function, Quart. J. Math. 17 (1) (1966) 39-43, ADS Abstracts.
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{k>0} (1-x^k)^k.
a(n) = -1/n*Sum_{k=1..n} sigma[2](k)*a(n-k).
G.f.: exp( Sum_{n>=1} -sigma_2(n)*x^n/n ). - Seiichi Manyama, Mar 04 2017
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, -add(
numtheory[sigma][2](j)*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..60); # Alois P. Heinz, Mar 12 2015
MATHEMATICA
nmax=50; CoefficientList[Series[Exp[Sum[-x^k/(k*(1-x^k)^2), {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 02 2015 *)
a[n_]:= a[n] = -1/n*Sum[DivisorSigma[2, k]*a[n-k], {k, 1, n}]; a[0]=1; Table[a[n], {n, 0, 100}] (* Vaclav Kotesovec, Mar 02 2015 *)
PROG
(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -n)
print([b(n) for n in range(55)]) # Peter Luschny, Nov 11 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Vladeta Jovovic, Aug 28 2002
STATUS
approved