OFFSET
0,6
COMMENTS
Previous name was: A simple grammar.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 726
FORMULA
E.g.f.: x^3*exp(x)^2 - 2*x^3*exp(x) + x^3.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (2*n^2+6*n+4)*a(n)+(-3*n^2+12)*a(n+1)+(-3*n+n^2+2)*a(n+2), a(5)= 120}.
For n<>3, a(n) = (2^n-16)*(n-2)*(n-1)*n/8. - Vaclav Kotesovec, Sep 30 2013
MAPLE
spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, Z, Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[x^3*(E^x-1)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(PARI) seq(n)={Vec(serlaplace(x^3*(exp(x + O(x^(n-3)))-1)^2), -(n+1))} \\ Andrew Howroyd, Jan 02 2020
CROSSREFS
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
Terms a(21) and beyond from Andrew Howroyd, Jan 02 2020
STATUS
approved