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%I A263072 #9 Mar 23 2016 04:54:36
%S A263072 1,1,8097453,9850349744182729,331910222316215755702672557,
%T A263072 134565509066155510620216211257550349401,
%U A263072 399017534874989738901076297624977315332337599285373,6213239693876579408708842528154872834110410698303331900339282569
%N A263072 Number of lattice paths from {10}^n to {0}^n using steps that decrement one or more components by one.
%C A263072 In general, row r > 0 of A262809 is asymptotic to sqrt(r*Pi) * (r^(r-1)/(r-1)!)^n * n^(r*n+1/2) / (2^(r/2) * exp(r*n) * (log(2))^(r*n+1)). - _Vaclav Kotesovec_, Mar 23 2016
%H A263072 Alois P. Heinz, <a href="/A263072/b263072.txt">Table of n, a(n) for n = 0..50</a>
%F A263072 a(n) ~ sqrt(10*Pi) * (10^9/9!)^n * n^(10*n+1/2) / (32 * exp(10*n) * (log(2))^(10*n+1)). - _Vaclav Kotesovec_, Mar 23 2016
%t A263072 With[{r = 10}, 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 A263072 Row n=10 of A262809.
%K A263072 nonn
%O A263072 0,3
%A A263072 _Alois P. Heinz_, Oct 08 2015

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