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%I #8 Mar 23 2016 04:55:10
%S 1,1,265729,3776339263873,756051015055329306625,
%T 1100327453912286201909924526081,
%U 7835213566547395052871069325808866414849,209691630817770382144439647416526247292909726379393,17469051230066445323872793284679234619523576313653708533767425
%N Number of lattice paths from {8}^n to {0}^n using steps that decrement one or more components by one.
%H Alois P. Heinz, <a href="/A263063/b263063.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) ~ sqrt(8*Pi) * (8^7/7!)^n * n^(8*n+1/2) / (16 * exp(8*n) * (log(2))^(8*n+1)). - _Vaclav Kotesovec_, Mar 23 2016
%t With[{r = 8}, 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=8 of A262809.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 08 2015
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