OFFSET
1,3
COMMENTS
Inverse binomial transform of A000203.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..3000
Vaclav Kotesovec, Graph abs(a(n)) / (n*2^n)
N. J. A. Sloane, Transforms
FORMULA
G.f.: (1/(1 + x))*Sum_{k>=1} k*x^k/((1 + x)^k - x^k).
L.g.f.: Sum_{k>=1} sigma(k)*x^k/(k*(1 + x)^k) = Sum_{n>=1} a(n)*x^n/n.
Conjecture: a(n) ~ (-1)^n * Pi^2/48 * n * 2^n. - Vaclav Kotesovec, Oct 16 2018
MAPLE
seq(add((-1)^(n-k)*binomial(n, k)*sigma(k), k=1..n), n=1..32); # Paolo P. Lava, Oct 25 2018
MATHEMATICA
Table[Sum[(-1)^(n - k) Binomial[n, k] DivisorSigma[1, k], {k, n}], {n, 32}]
nmax = 32; Rest[CoefficientList[Series[1/(1 + x) Sum[k x^k/((1 + x)^k - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
PROG
(GAP) Flat(List([1..10], n->Sum([1..n], k->(-1)^(n-k)*Binomial(n, k)*Sigma(k)))); # Muniru A Asiru, Oct 15 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 15 2018
STATUS
approved