OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>=1} x^k/(k*(1 - x^k)^2).
E.g.f.: -log(Product_{k>=1} (1 - x^k)^k).
E.g.f.: A(x) = log(B(x)), where B(x) = o.g.f. of A000219.
a(p^k) = (p^(2*k+2) - 1)*(p^k - 1)!/(p^2 - 1), where p is a prime.
MATHEMATICA
Table[(n - 1)! DivisorSigma[2, n], {n, 1, 22}]
nmax = 22; Rest[CoefficientList[Series[Sum[x^k/(k (1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
nmax = 22; Rest[CoefficientList[Series[-Log[Product[(1 - x^k)^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!]
PROG
(PARI) a(n) = (n-1)!*sigma(n, 2); \\ Michel Marcus, Aug 22 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 22 2018
STATUS
approved