login
Diagonal terms in the expansion of (1+x*y+y*z+z*x)/(1-x-y-z).
1

%I #16 Oct 31 2020 02:54:05

%S 1,9,126,2310,47250,1027026,23207184,538748496,12757863690,

%T 306752696250,7465133615940,183458150153460,4545211223957040,

%U 113378500045162800,2844670649392440000,71731904712206892480,1816739665054871280570,46189610653753780435530,1178358502858339948645500

%N Diagonal terms in the expansion of (1+x*y+y*z+z*x)/(1-x-y-z).

%C Expand that rational function as Sum_i Sum_j Sum_k c(i,j,k)*x^i*y^j*z^k; then a(n) = c(n,n,n).

%F a(n) = (4*n - 1) * (3*n)! / ((3*n - 1) * n!^3). - _Vaclav Kotesovec_, Oct 28 2020

%t nmax = 20; Flatten[{1, Table[Coefficient[Series[(1+x*y+y*z+z*x)/(1-x-y-z), {x, 0, n}, {y, 0, n}, {z, 0, n}], x^n*y^n*z^n], {n, 1, nmax}]}] (* _Vaclav Kotesovec_, Oct 23 2020 *)

%Y Cf. A006480, A338075.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 22 2020

%E More terms from _Vaclav Kotesovec_, Oct 23 2020