This site is supported by donations to The OEIS Foundation.

 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!)
 A101054 E.g.f.: exp(exp(x)-1)/(1-x)^2. 4
 1, 3, 12, 59, 343, 2302, 17537, 149711, 1417444, 14755947, 167664955, 2066153410, 27460121377, 391670868279, 5969233120520, 96827494235555, 1665874346755107, 30302732222472482, 581141491978752769, 11719848107849221435, 247960209086201040552, 5491993051193586857235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence appears in the problem of normal ordering of functions of boson operators. LINKS G. C. Greubel, Table of n, a(n) for n = 0..447 FORMULA a(n) = ((-1)^n*n!/e)*Sum_{k>=0} L(n,-n-2,k)/k!, where L is a generalized Laguerre polynomial. a(n) = Sum_{k=0..n} binomial(n,k)*(k + 1)!*Bell(n-k), where Bell() = A000110. - Ilya Gutkovskiy, May 24 2018 MAPLE egf := exp(exp(x)-1)/((1-x)^2); seq(n!*coeff(series(egf, x, n+1), x, n), n=0..21); # Peter Luschny, Sep 17 2014 MATHEMATICA With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x] - 1]/(1 - x)^2, {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, May 23 2018 *) PROG (PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)-1)/(1-x)^2 )) \\ G. C. Greubel, May 23 2018 (MAGMA) m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(Exp(x)-1)/(1-x)^2)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 23 2018 CROSSREFS Cf. A000110, A101053. Sequence in context: A196710 A196711 A304788 * A122752 A020102 A277179 Adjacent sequences:  A101051 A101052 A101053 * A101055 A101056 A101057 KEYWORD nonn AUTHOR Karol A. Penson, Nov 29 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.

Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)