|
|
A288385
|
|
Expansion of Product_{k>=1} (1 - x^k)^sigma(k).
|
|
6
|
|
|
1, -1, -3, -1, 0, 10, 8, 12, 1, -28, -29, -67, -51, -28, 79, 163, 256, 343, 273, 136, -351, -649, -1446, -1751, -1889, -1453, -124, 1924, 5138, 7608, 10636, 10903, 10054, 3143, -5799, -20521, -37217, -53057, -65661, -66086, -54430, -15648, 37179, 122732
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A001001(k)*a(n-k) for n > 0.
G.f.: exp(-Sum_{k>=1} sigma_2(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 29 2018
|
|
MAPLE
|
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
d*sigma(d), d=divisors(j))*b(n-j), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i)*a(i), i=0..n-1))
end:
|
|
MATHEMATICA
|
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*DivisorSigma[1, d], {d,
Divisors[j]}]*b[n - j], {j, 1, n}]/n];
a[n_] := a[n] = If[n == 0, 1, -Sum[b[n - i]*a[i], {i, 0, n - 1}]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|