login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320349 Expansion of e.g.f. Product_{k>=1} 1/(1 - log(1/(1 - x))^k). 8
1, 1, 5, 32, 278, 2894, 35986, 514128, 8306448, 149558688, 2968216944, 64314676128, 1510065781968, 38178537908016, 1033794746169168, 29840453678758272, 914461132860063360, 29645845798652997120, 1013511411165693991680, 36436289007997132646400, 1373976152501162688288000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..413

FORMULA

E.g.f.: exp(Sum_{k>=1} sigma(k)*log(1/(1 - x))^k/k).

a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A000041(k)*k!.

From Vaclav Kotesovec, Oct 13 2018: (Start)

a(n) ~ n! * exp(n + Pi*sqrt(2*n/(3*(exp(1) - 1))) + Pi^2/(12*(exp(1) - 1))) / (4 * sqrt(3) * n * (exp(1) - 1)^n).

a(n) ~ sqrt(Pi) * exp(Pi*sqrt(2*n/(3*(exp(1) - 1))) + Pi^2/(12*(exp(1) - 1))) * n^(n - 1/2) / (2^(3/2) * sqrt(3) * (exp(1) - 1)^n).

(End)

MAPLE

seq(n!*coeff(series(mul(1/(1-log(1/(1-x))^k), k=1..100), x=0, 21), x, n), n=0..20); # Paolo P. Lava, Jan 09 2019

MATHEMATICA

nmax = 20; CoefficientList[Series[Product[1/(1 - Log[1/(1 - x)]^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 20; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] Log[1/(1 - x)]^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[Abs[StirlingS1[n, k]] PartitionsP[k] k!, {k, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A000041, A000203, A048994, A053529, A167137, A306042, A320350.

Sequence in context: A328055 A265130 A305407 * A001923 A257710 A305305

Adjacent sequences:  A320346 A320347 A320348 * A320350 A320351 A320352

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 11 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)