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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101053 a(n) = n!*Sum_{k=0..n} Bell(k)/k! (cf. A000110). 6
1, 2, 6, 23, 107, 587, 3725, 26952, 219756, 1998951, 20105485, 221838905, 2666280457, 34689290378, 485840964614, 7288997427755, 116634438986227, 1982868327635663, 35692311974248093, 678159760252918824, 13563246929216611852, 284828660383365005643 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence was originally defined as an infinite sum involving generalized Laguerre polynomials: a(n)= ((-1)^n*n!/exp(1))*Sum_{k>=0} LaguerreL(n,-n-1,k)/k!, n=0,1... . It appears in the problem of normal ordering of functions of boson operators.

a(n) is the number of ways to linearly order the elements in a (possibly empty) subset S of {1,2,...,n} and then partition the complement of S. - Geoffrey Critzer, Aug 07 2015

LINKS

Robert Israel, Table of n, a(n) for n = 0..450

FORMULA

E.g.f: exp(exp(x)-1)/(1-x).

MAPLE

with(combinat): a:=n->add(bell(j)*n!/j!, j=0..n): seq(a(n), n=0..20); # Zerinvary Lajos, Mar 19 2007

MATHEMATICA

nn = 21; Range[0, nn]! CoefficientList[Series[Exp[(Exp[x]-1)]/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Aug 07 2015 *)

PROG

(PARI) egf(s)=my(v=Vec(s), i); while(polcoeff(s, i)==0, i++); i--; vector(i+#v, j, polcoeff(s, j+i)*(j+i)!)

egf(exp(exp(x)-1)/(1-x)) \\ Charles R Greathouse IV, Aug 07 2015

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(exp(x)-1)/(1-x) )) \\ G. C. Greubel, Mar 31 2019

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Exp(x)-1)/(1-x) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Mar 31 2019

(Sage) m = 30; T = taylor(exp(exp(x)-1)/(1-x), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Mar 31 2019

CROSSREFS

Cf. A000110.

Sequence in context: A113226 A071075 A007555 * A155857 A071076 A297196

Adjacent sequences:  A101050 A101051 A101052 * A101054 A101055 A101056

KEYWORD

nonn

AUTHOR

Karol A. Penson, Nov 29 2004

EXTENSIONS

New definition from Vladeta Jovovic, Dec 01 2004

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 November 16 22:05 EST 2019. Contains 329208 sequences. (Running on oeis4.)