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%I #8 Mar 23 2016 04:54:56
%S 1,1,1462563,191731486403293,496505991344667030490635,
%T 12024609569670508078686022988554381,
%U 1742079663955078309800553960117733249663480043,1121241285685659360225420876424590015281785102622410968973
%N Number of lattice paths from {9}^n to {0}^n using steps that decrement one or more components by one.
%H Alois P. Heinz, <a href="/A263071/b263071.txt">Table of n, a(n) for n = 0..50</a>
%F 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
%t 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 *)
%Y Row n=9 of A262809.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 08 2015
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