|
|
A052856
|
|
E.g.f.: (1-3*exp(x)+exp(2*x))/(exp(x)-2).
|
|
10
|
|
|
1, 2, 4, 14, 76, 542, 4684, 47294, 545836, 7087262, 102247564, 1622632574, 28091567596, 526858348382, 10641342970444, 230283190977854, 5315654681981356, 130370767029135902, 3385534663256845324
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Previous name was: A simple grammar.
Stirling transform of A005212(n-1)=[1,1,0,6,0,120,0,...] is a(n-1)=[1,2,4,14,76,...]. - Michael Somos, Mar 04 2004
Stirling transform of (-1)^n*A052612(n-1)=[0,2,-2,12,-24,...] is a(n-1)=[0,2,4,14,76,...]. - Michael Somos, Mar 04 2004
Stirling transform of A000142(n)=[2,2,6,24,120,...] is a(n)=[2,2,4,14,76,...]. - Michael Somos, Mar 04 2004
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: (1-3*exp(x)+exp(x)^2)/(-2+exp(x))
|
|
MAPLE
|
spec := [S, {B=Sequence(C), C=Set(Z, 1 <= card), S=Union(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
With[{nn=20}, CoefficientList[Series[(1-3Exp[x]+Exp[x]^2)/(-2+Exp[x]), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Nov 24 2012 *)
|
|
PROG
|
(PARI) a(n)=if(n<0, 0, n!*polcoeff(subst(y+1/(1-y), y, exp(x+x*O(x^n))-1), n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|