login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300673 Expansion of e.g.f. exp(Sum_{k>=1} mu(k)*x^k/k!), where mu() is the Moebius function (A008683). 0
1, 1, 0, -3, -6, 5, 61, 126, -308, -2772, -5669, 25630, 224730, 486551, -3068155, -29264219, -72173176, 513535711, 5625869262, 16687752839, -113740116822, -1496118902963, -5508392724427, 31534346503605, 523333047780288, 2414704077547660, -10254467367668159 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Exponential transform of A008683.

LINKS

Table of n, a(n) for n=0..26.

N. J. A. Sloane, Transforms

FORMULA

E.g.f.: exp(Sum_{k>=1} A008683(k)*x^k/k!).

EXAMPLE

E.g.f.: A(x) = 1 + x/1! - 3*x^3/3! - 6*x^4/4! + 5*x^5/5! + 61*x^6/6! + 126*x^7/7! - 308*x^8/8! - 2772*x^9/9! - 5669*x^10/10! + ...

MATHEMATICA

nmax = 26; CoefficientList[Series[Exp[Sum[MoebiusMu[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Sum[MoebiusMu[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 26}]

CROSSREFS

Cf. A008683, A050385, A050386, A068341, A073776, A104688, A117209, A117210, A195589, A204290, A300663.

Sequence in context: A303564 A121867 A307132 * A009193 A144253 A138743

Adjacent sequences:  A300670 A300671 A300672 * A300674 A300675 A300676

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 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 April 3 01:39 EDT 2020. Contains 333195 sequences. (Running on oeis4.)