OFFSET
0,6
LINKS
G.-B. Chae, E. M. Palmer, R. W. Robinson, Counting labeled cubic graphs, Disc. Math. 307 (2007) 2979-2992, g(s,d).
FORMULA
T(3s,0) = A007099(s).
EXAMPLE
The triangle starts
0;
0, 0;
0, 0, 6;
0, 0, 0, 120;
0, 0, 0, 0, 5040;
0, 0,180, 0, 0, 362880;
1, 0, 0, 23520, 0, 0, 39916800;
MAPLE
# expand g(s, d) of eq (21) of Chae et al.
g2x := 6*x^5/4! ;
for itr from 1 to 16 do
g2xx := expand(diff(g2x, x)) ;
g2x := (x^5-x^8)*g2x*g2xx+(x^4-2*x^7+x^10+x^5*y-x^8*y)/2*g2xx
+(2*x^4+x^7)*g2x^2
+(8*x^3-6*x^6-x^9+x^12+2*x*y-2*x^4*y+8*x^7*y-2*x^10*y)/2*g2x
+ x^5/4 -3*x^8/4 +3*x^11/4-x^14/4 +3*x^6*y/2-9*x^9*y/4+3*x^12*y/4+x*y^2/2
-x^4*y^2+7*x^7*y^2/4-x^10*y^2/2 ;
g2x := expand(%) ;
g2x := taylor(g2x, x=0, itr+5) ;
g2x := convert(g2x, polynom) ;
g2 := expand(int(g2x, x)) ;
for s from 0 to itr+1 do
g := coeftayl(g2, x=0, s) ;
for d from 0 to s do
twon := (2*s+4*d)/3 ;
coeftayl(g, y=0, d) ;
printf("%a, ", %*twon!) ;
end do:
printf("\n") ;
end do:
end do:
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Dec 05 2018
STATUS
approved