OFFSET
0,2
COMMENTS
Expand the rational function 1/(1-x-2*y-3*z) as Sum_i Sum_j Sum_k c(i,j,k)*x^i*y^j*z^k; a(n) = c(n,n,n).
LINKS
Robert Israel, Table of n, a(n) for n = 0..250
FORMULA
Conjectures from Robert Israel, Oct 25 2020: (Start)
a(n+1) = 18*(3*n+1)*(3*n+2)*a(n)/(n+1)^2.
G.f.: hypergeom([1/3, 2/3], [1], 162*x). (End)
a(n) = 6^n * (3*n)! / n!^3. - Vaclav Kotesovec, Oct 28 2020
MAPLE
N:= 25: # for a(0)..a(N)
F:= 1/(1-x-2*y-3*z):
S1:= series(F, x, N+1):
L1:= [seq(coeff(S1, x, i), i=0..N)]:
L2:= [seq(coeff(series(L1[i+1], y, i+1), y, i), i=0..N)]:
seq(coeff(series(L2[i+1], z, i+1), z, i), i=0..N); # Robert Israel, Oct 24 2020
MATHEMATICA
nmax = 20; Flatten[{1, Table[Coefficient[Series[1/(1-x-2*y-3*z), {x, 0, n}, {y, 0, n}, {z, 0, n}], x^n*y^n*z^n], {n, 1, nmax}]}] (* Vaclav Kotesovec, Oct 23 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 22 2020
EXTENSIONS
More terms from Vaclav Kotesovec, Oct 23 2020
STATUS
approved