OFFSET
0,5
COMMENTS
Previous name was: A simple grammar.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..448
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 709
FORMULA
E.g.f.: log(-1/(-1+x))^4.
Recurrence: {a(1)=0, a(0)=0, a(2)=0, (1+4*n+6*n^2+4*n^3+n^4)*a(n+1) + (-4*n^3-15-18*n^2-28*n)*a(n+2) + (6*n^2+24*n+25)*a(n+3) + (-4*n-10)*a(n+4)+a(n+5), a(3)=0, a(4)=24}.
a(n) ~ (n-1)! * 2*log(n)*(2*log(n)^2 + 6*gamma*log(n) - Pi^2 + 6*gamma^2), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 30 2013
a(n) = 24*A000454(n) = 4!*(-1)^n*Stirling1(n,4). - Andrew Howroyd, Jul 27 2020
MAPLE
spec := [S, {B=Cycle(Z), S=Prod(B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[(Log[1-x])^4, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(PARI) x='x+O('x^30); concat(vector(4), Vec(serlaplace((log(1-x))^4))) \\ G. C. Greubel, Aug 30 2018
(PARI) a(n) = {4!*stirling(n, 4, 1)*(-1)^n} \\ Andrew Howroyd, Jul 27 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f., Vaclav Kotesovec, Sep 30 2013
STATUS
approved