The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A052766 Expansion of e.g.f.: (log(1-x))^2*x^3. 3
 0, 0, 0, 0, 0, 120, 720, 4620, 33600, 276192, 2540160, 25874640, 289301760, 3523208832, 46425899520, 658169366400, 9988896153600, 161590513766400, 2775695618949120, 50455787382604800, 967644983144448000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Previous name was: A simple grammar. LINKS G. C. Greubel, Table of n, a(n) for n = 0..449 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 723 FORMULA E.g.f.: log(-1/(-1+x))^2*x^3. Recurrence: a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=120, (n^4-7*n^2-3*n^3+15*n+18)*a(n) + (8*n-2*n^3+5*n^2-20)*a(n+1) + (-3*n+n^2+2)*a(n+2) = 0. a(n) ~ 2*(n-1)! * (log(n) + gamma), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 30 2013 a(n) = n*A052754(n-1) = 2*n*(n-1)*(n-2)*abs(Stirling1(n-3,2)) for n >= 3. - Andrew Howroyd, Aug 08 2020 MAPLE spec := [S, {B=Cycle(Z), S=Prod(Z, Z, Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA CoefficientList[Series[(Log[1-x])^2*x^3, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *) Join[{0, 0, 0, 0, 0}, RecurrenceTable[{a[5] == 120, a[6] == 720, (n^4 -7*n^2 -3*n^3 +15*n +18)*a[n] + (8*n -2*n^3 +5*n^2 -20)*a[n+1] == -(-3*n +n^2 + 2)*a[n+2]}, a, {n, 5, 30}]] (* G. C. Greubel, Sep 05 2018 *) PROG (PARI) x='x+O('x^30); concat(vector(5), Vec(serlaplace(log(-1/(-1+x))^2*x^3))) \\ G. C. Greubel, Sep 05 2018 (PARI) a(n)={if(n>=3, 2*n*(n-1)*(n-2)*abs(stirling(n-3, 2, 1)), 0)} \\ Andrew Howroyd, Aug 08 2020 CROSSREFS Cf. A052754, A052759. Sequence in context: A292970 A052769 A179724 * A052627 A251264 A206025 Adjacent sequences: A052763 A052764 A052765 * A052767 A052768 A052769 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS New name, using e.g.f., by Vaclav Kotesovec, Sep 30 2013 STATUS approved

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

Last modified December 8 07:38 EST 2022. Contains 358691 sequences. (Running on oeis4.)