A263071 Number of lattice paths from {9}^n to {0}^n using steps that decrement one or more components by one.

1, 1, 1462563, 191731486403293, 496505991344667030490635, 12024609569670508078686022988554381, 1742079663955078309800553960117733249663480043, 1121241285685659360225420876424590015281785102622410968973

Offset: 0

Author

Alois P. Heinz, Oct 08 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Row n=9 of A262809.

Programs

Mathematica

With[{r = 9}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 10}]}]] (* Vaclav Kotesovec, Mar 22 2016 *)

Formula

a(n) ~ 3*sqrt(Pi) * (9^8/8!)^n * n^(9*n+1/2) / (2^(9/2) * exp(9*n) * (log(2))^(9*n+1)). - Vaclav Kotesovec, Mar 23 2016