OFFSET
1,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..400
FORMULA
E.g.f.: -Sum_{k>=1} log(1 - log(1 + x)^(2*k - 1)).
E.g.f.: A(x) = log(B(x)), where B(x) = e.g.f. of A298905.
exp(Sum_{n>=1} a(n) * (exp(x) - 1)^n / n!) = g.f. of A000009.
a(n) = Sum_{k=1..n} Stirling1(n,k) * (k - 1)! * A000593(k).
E.g.f.: Sum_{k>=1} log(1 + log(1 + x)^k). - Vaclav Kotesovec, Dec 15 2019
Conjecture: a(n) ~ n! * (-1)^(n+1) * Pi^2 * exp(n) / (24 * (exp(1) - 1)^(n+1)). - Vaclav Kotesovec, Dec 16 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Sum[(-1)^(k + 1) Log[1 + x]^k/(k (1 - Log[1 + x]^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS1[n, k] (k - 1)! Sum[Mod[d, 2] d, {d, Divisors[k]}], {k, 1, n}], {n, 1, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[Log[1 + Log[1 + x]^k], {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Dec 15 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 12 2019
STATUS
approved