A338077 - OEIS

A338077

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

1, 9, 126, 2310, 47250, 1027026, 23207184, 538748496, 12757863690, 306752696250, 7465133615940, 183458150153460, 4545211223957040, 113378500045162800, 2844670649392440000, 71731904712206892480, 1816739665054871280570, 46189610653753780435530, 1178358502858339948645500

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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).

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = (4*n - 1) * (3*n)! / ((3*n - 1) * n!^3). - Vaclav Kotesovec, Oct 28 2020

MATHEMATICA

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 *)

CROSSREFS

Cf. A006480, A338075.

Sequence in context: A234573 A306033 A065707 * A034301 A092651 A366036

Adjacent sequences: A338074 A338075 A338076 * A338078 A338079 A338080

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 22 2020

EXTENSIONS

More terms from Vaclav Kotesovec, Oct 23 2020

STATUS

approved