OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..420
FORMULA
E.g.f.: -Sum_{k>=1} log(1 - (exp(x) - 1)^k).
E.g.f.: A(x) = log(B(x)), where B(x) = e.g.f. of A167137.
G.f.: Sum_{k>=1} (k - 1)! * sigma(k) * x^k / Product_{j=1..k} (1 - j*x), where sigma = A000203.
exp(Sum_{n>=1} a(n) * log(1 + x)^n / n!) = g.f. of the partition numbers (A000041).
a(n) = Sum_{k=1..n} Stirling2(n,k) * (k - 1)! * sigma(k).
a(n) ~ n! * Pi^2 / (12 * (log(2))^(n+1)). - Vaclav Kotesovec, Dec 14 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Sum[(Exp[x] - 1)^k/(k (1 - (Exp[x] - 1)^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS2[n, k] (k - 1)! DivisorSigma[1, k], {k, 1, n}], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 11 2019
STATUS
approved