OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..420
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)
FORMULA
E.g.f.: Sum_{i>=1} Sum_{j>=1} (exp(x) - 1)^(i*j) / (i*j).
E.g.f.: log(Product_{k>=1} 1 / (1 - (exp(x) - 1)^k)^(1/k)).
G.f.: Sum_{k>=1} (k - 1)! * tau(k) * x^k / Product_{j=1..k} (1 - j*x), where tau = A000005.
a(n) = Sum_{k=1..n} Stirling2(n,k) * (k - 1)! * tau(k).
a(n) ~ n! * (log(n) + 2*gamma - log(2) - log(log(2))) / (n * (log(2))^n), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 14 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[-Sum[Log[1 - (Exp[x] - 1)^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS2[n, k] (k - 1)! DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 11 2019
STATUS
approved